A371826 a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-k,n-2*k).

1, 2, 8, 35, 170, 872, 4740, 26994, 161006, 1001009, 6476976, 43480373, 302250196, 2170406149, 16070240276, 122453910495, 958755921686, 7701233828576, 63381318474768, 533793776053926, 4595440308780620, 40400161269188412, 362367733795887848

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = [x^n] 1/((1-x-n*x^2) * (1-x)^n).

a(n) ~ exp(3*sqrt(n)/2) * n^(n/2) / 2. - Vaclav Kotesovec, Apr 07 2024

Prog

(PARI) a(n) = sum(k=0, n\2, n^k*binomial(2*n-k, n-2*k));

Crossrefs

Cf. A371825, A371827.

Cf. A171180.

Sequence in context: A007034 A011791 A259757 * A347953 A030847 A030929

Adjacent sequences: A371821 A371824 A371825 * A371827 A371828 A371829

Keyword

nonn

Author

Seiichi Manyama, Apr 07 2024

Status

approved