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
Keywords
Programs
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Maple
a := n -> add(A008288(n, k)*n^k, k=0..n): seq(a(n), n=0..19);
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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}]
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