A345876 a(n) = Sum_{k=0..n} binomial(2*n, n-k) * k^n.

1, 1, 8, 90, 1408, 28350, 697344, 20264244, 679313408, 25805186550, 1095482736640, 51397070440716, 2640925289349120, 147491783753286700, 8895880971425939456, 576279075821454657000, 39905347440408027725824, 2941534126495441574472870, 229966392623413457628168192

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..360

Formula

a(n) ~ 2^(2*n + 1/2) * r^(n+1) * n^n / (sqrt(1 + r^2) * exp(n) * (1 - r^2)^n), where r = 0.647918229029602749602061258113970414114660380467168496836586... is the positive root of the equation (1 + r) = (1 - r)*exp(1/r).

Mathematica

Join[{1}, Table[Sum[Binomial[2*n, n-k]*k^n, {k, 0, n}], {n, 1, 20}]]

Prog

(PARI) a(n) = sum(k=0, n, binomial(2*n, n-k) * k^n); \\ Michel Marcus, Oct 03 2021

Crossrefs

Cf. A072034, A298851.

Sequence in context: A187667 A331512 A092956 * A295623 A319174 A034667

Adjacent sequences: A345873 A345874 A345875 * A345877 A345878 A345879

Keyword

nonn

Author

Vaclav Kotesovec, Oct 03 2021

Status

approved