A070075 Stirling transform of A021009.

1, 2, 9, 57, 464, 4593, 53381, 711056, 10665071, 177698377, 3253933294, 64917524367, 1400923403957, 32503510579738, 806599849548101, 21313355891736741, 597326671763101944

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..410

Formula

In Maple notation, a(0)=1, a(n)= sum(stirling2(n, k)*k!*LaguerreL(k, -1), k=1..n), n=1, 2... . E.g.f.: exp((exp(x)-1)/(2-exp(x)))/(2-exp(x))

a(n) ~ exp(1/(4*log(2)) - 3/4 + sqrt(2*n/log(2)) - n) * n^(n + 1/4) / (2^(5/4) * (log(2))^(n + 3/4)). - Vaclav Kotesovec, Nov 13 2017

Mathematica

Flatten[{1, Table[Sum[StirlingS2[n, k]*k!*LaguerreL[k, -1], {k, 1, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Nov 13 2017 *)

Crossrefs

Cf. A021009.

Sequence in context: A175912 A218824 A111545 * A124405 A300343 A141787

Adjacent sequences: A070072 A070073 A070074 * A070076 A070077 A070078

Keyword

nonn

Author

Karol A. Penson, Apr 22 2002

Status

approved