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Partial sums of the central Stirling numbers of the second kind.
1

%I #12 May 11 2014 16:55:21

%S 1,2,9,99,1800,44325,1367977,50697257,2192461310,108367857065,

%T 6025952821720,372308453692006,25302513044450266,1875871087298000326,

%U 150658859151673309726,13030526931922299349726,1207492044401730133131811

%N Partial sums of the central Stirling numbers of the second kind.

%H Vincenzo Librandi, <a href="/A187647/b187647.txt">Table of n, a(n) for n = 0..49</a>

%F a(n) = sum_{k=0..n} A048993(2*k,k).

%F a(n+1)-a(n) = A007820(n+1).

%F a(n) ~ n^n * 2^(2*n) / (sqrt(2*Pi*(1-c)*n) * exp(n) * (2-c)^n * c^n), where c = -LambertW(-2*exp(-2)). - _Vaclav Kotesovec_, May 11 2014

%p seq(sum(combinat[stirling2](2*k,k),k=0..n),n=0..12);

%t Table[Sum[StirlingS2[2k, k], {k, 0, n}], {n, 0, 16}]

%o (Maxima) makelist(sum(stirling2(2*k,k),k,0,n),n,0,12);

%Y Cf. A007820, A226775.

%K nonn,easy

%O 0,2

%A _Emanuele Munarini_, Mar 12 2011