A376871 a(n) = Sum_{k=0..n} n^k * hypergeom([-k, k - n], [1], 2).

1, 2, 11, 88, 941, 12546, 200479, 3735264, 79524793, 1905008050, 50720779691, 1486111590360, 47524305052069, 1647275572867666, 61522053792814679, 2463133651846231936, 105244572157172848369, 4780359272226823337250, 230016032074517010618403, 11688053305141450955275800

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) is the Delannoy polynomial D(n, x) evaluated at x = n.

a(n) ~ exp(2) * n^n. - Vaclav Kotesovec, Oct 13 2024

Maple

a := n -> add(A008288(n, k)*n^k, k=0..n):
seq(a(n), n=0..19);

Mathematica

Unprotect[Power]; Power[0, 0] = 1; Protect[Power];
a[n_] := Sum[n^k Hypergeometric2F1[-k, k - n, 1, 2], {k, 0, n}];
Table[a[n], {n, 0, 19}]

Crossrefs

D(n, 1) = A000128(n + 1), D(n, -1) = A056594(n).

Cf. A008288.

Sequence in context: A138739 A216831 A221864 * A197900 A106961 A215623

Adjacent sequences: A376868 A376869 A376870 * A376872 A376873 A376874

Keyword

nonn

Author

Peter Luschny, Oct 12 2024

Status

approved