A367256 a(n) = Sum_{k=0..n} binomial(n, k) * binomial(n - 1, k - 1) * n^(n - k).

1, 1, 5, 46, 593, 9726, 192637, 4457580, 117769409, 3492894070, 114790042901, 4137157889316, 162154385331985, 6863637142316332, 311905306734621069, 15140756439172826776, 781693659313991730945, 42759819036520142319270, 2469943332976774829606821

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..350

Formula

a(n) = Sum_{k=0..n} A367267(n, k) * n^(n - k).

a(n) = n*n^(n - 1)*hypergeom([1 - n, 1 - n], [2], 1/n) for n > 0.

a(n) ~ exp(2*sqrt(n) - 1) * n^(n - 3/4) / (2*sqrt(Pi)). - Vaclav Kotesovec, Nov 11 2023

Maple

a := n -> if n= 0 then 1 else n*n^(n - 1)*hypergeom([1 - n, 1 - n], [2], 1/n) fi:
seq(simplify(a(n)), n = 0..19);

Mathematica

A367256[n_] := If[n == 0, 1, n*n^(n-1)*Hypergeometric2F1[1-n, 1-n, 2, 1/n]];
Array[A367256, 25, 0] (* Paolo Xausa, Jan 31 2024 *)

Crossrefs

Cf. A187021, A367267, A367257.

Sequence in context: A371380 A295544 A058478 * A159608 A167559 A367154

Adjacent sequences: A367253 A367254 A367255 * A367257 A367258 A367259

Keyword

nonn

Author

Peter Luschny, Nov 11 2023

Status

approved