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%I #7 Nov 13 2017 09:57:53
%S 1,2,9,57,464,4593,53381,711056,10665071,177698377,3253933294,
%T 64917524367,1400923403957,32503510579738,806599849548101,
%U 21313355891736741,597326671763101944
%N Stirling transform of A021009.
%H Vaclav Kotesovec, <a href="/A070075/b070075.txt">Table of n, a(n) for n = 0..410</a>
%F 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))
%F 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
%t Flatten[{1, Table[Sum[StirlingS2[n, k]*k!*LaguerreL[k, -1], {k,1,n}], {n,1,20}]}] (* _Vaclav Kotesovec_, Nov 13 2017 *)
%Y Cf. A021009.
%K nonn
%O 0,2
%A _Karol A. Penson_, Apr 22 2002
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