A335390 a(n) = Sum_{k=0..n} Stirling2(n,k) * 2^binomial(k,2).

1, 1, 3, 15, 127, 1895, 53071, 2953575, 337064047, 79446381319, 38491200186831, 38046637826801703, 76226441027901385519, 308075833912652114006087, 2503633988838391023366024079, 40826169678526460459483237927271, 1334110729147927667553970495057395439

Offset: 0

Author

Ilya Gutkovskiy, Jun 04 2020

Keywords

• nonn

Comments

Stirling transform of A006125.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..82

Crossrefs

Cf. A006024, A006125.

Programs

Maple

a:= n-> add(Stirling2(n, k)*2^(k*(k-1)/2), k=0..n):
seq(a(n), n=0..19);  # Alois P. Heinz, Jun 05 2020

Mathematica

Table[Sum[StirlingS2[n, k] 2^Binomial[k, 2], {k, 0, n}], {n, 0, 16}]

PARI

a(n) = sum(k=0, n, stirling(n,k,2) * 2^binomial(k,2)); \\ Michel Marcus, Jun 05 2020

Formula

G.f.: Sum_{k>=0} 2^binomial(k,2) * x^k / Product_{j=1..k} (1 - j*x).

E.g.f.: Sum_{k>=0} 2^binomial(k,2) * (exp(x) - 1)^k / k!.

a(n) ~ 2^(n*(n-1)/2). - Vaclav Kotesovec, Jun 05 2020