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A070075 Stirling transform of A021009. 1
1, 2, 9, 57, 464, 4593, 53381, 711056, 10665071, 177698377, 3253933294, 64917524367, 1400923403957, 32503510579738, 806599849548101, 21313355891736741, 597326671763101944 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)