The 2-adic valuation of a sequence arising from a rational integral. (English) Zbl 1210.11123
The authors study properties of the 2-adic valuation of an integer sequence that originates from an explicit evaluation of a quartic integral (for details see [G. Boros and V. H. Moll, J. Comput. Appl. Math. 106, No. 2, 361–368 (1999; Zbl 0939.33007)]). They generalize a result of G. Boros, V. H. Moll and J. Shallit [Sci., Ser. A, Math. Sci. (N.S.) 7(2001), 37–50 (2002; Zbl 1121.11022)] and also give a combinatorial interpretation of the valuations of this sequence.
Reviewer: Olaf Ninnemann (Berlin)
MSC:
| 11S85 | Other nonanalytic theory |
| 05A15 | Exact enumeration problems, generating functions |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 33E20 | Other functions defined by series and integrals |
References:
| [1] | Amdeberhan, T.; Manna, D.; Moll, V., The 2-adic valuation of Stirling numbers, Experiment. Math., 17, 69-82 (2008) · Zbl 1218.11024 |
| [2] | T. Amdeberhan, V. Moll, A formula for a quartic integral: A survey of old proofs and some new ones, Ramanujan J., 2008, in press; T. Amdeberhan, V. Moll, A formula for a quartic integral: A survey of old proofs and some new ones, Ramanujan J., 2008, in press · Zbl 1178.33002 |
| [3] | Boros, G.; Moll, V., A criterion for unimodality, Electron. J. Combin., 6, 1-6 (1999) · Zbl 0911.05004 |
| [4] | Boros, G.; Moll, V., An integral hidden in Gradshteyn and Ryzhik, J. Comput. Appl. Math., 106, 361-368 (1999) · Zbl 0939.33007 |
| [5] | Boros, G.; Moll, V.; Shallit, J., The 2-adic valuation of the coefficients of a polynomial, Scientia Ser. A, 7, 37-50 (2001) · Zbl 1121.11022 |
| [6] | Kauers, M.; Paule, P., A computer proof of Moll’s log-concavity conjecture, Proc. Amer. Math. Soc., 135, 3837-3846 (2007) · Zbl 1126.33009 |
| [7] | Lengyel, T., On the divisibility by 2 of the Stirling numbers of the second kind, Fibonacci Quart., 32, 194-201 (1994) · Zbl 0808.11017 |
| [8] | Moll, V., The evaluation of integrals: A personal story, Notices Amer. Math. Soc., 49, 311-317 (2002) · Zbl 1126.11347 |
| [9] | Petkovsek, M.; Wilf, H.; Zeilberger, D., \(A = B (1996)\), A.K. Peters, Ltd. · Zbl 0848.05002 |
| [10] | De Wannemacker, S., On the 2-adic orders of Stirling numbers of the second kind, Integers, 5, 1 (2005), A-21 · Zbl 1093.11015 |
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