OFFSET
0,5
COMMENTS
This is a variant of A039755 with reflected rows. - Tilman Piesk, Oct 27 2019
LINKS
Alois P. Heinz, Rows n = 0..100, flattened
Paweł Hitczenko, A class of polynomial recurrences resulting in (n/log n, n/log^2 n)-asymptotic normality, arXiv:2403.03422 [math.CO], 2024. See p. 8.
Ruedi Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.
FORMULA
Sum a(n,n-k) x^n*y^k/n! = exp(x + y/2*(exp(2*x) - 1)).
T(n, k) = A039755(n, n-k). - Tilman Piesk, Oct 27 2019
EXAMPLE
1;
1, 1;
1, 4, 1;
1, 9, 13, 1;
1, 16, 58, 40, 1;
1, 25, 170, 330, 121, 1;
1, 36, 395, 1520, 1771, 364, 1;
1, 49, 791, 5075, 12411, 9219, 1093, 1;
PROG
(PARI) T(n, k)=if(k<0||k>n, 0, n!*polcoeff(polcoeff(exp(x*y+(exp(2*x*y+x*O(x^n))-1)/(2*y)), n), k))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ruedi Suter (suter(AT)math.ethz.ch)
STATUS
approved