A187648 - OEIS

%I #15 May 27 2017 19:50:29

%S 1,2,13,238,7007,276332,13615867,804559020,55435688573,4363540990502,

%T 386285596492697,37986820683352442,4108370877690921963,

%U 484652929620424467088,61930188031979540102743,8521504634108297687933368

%N Partial sums of the (signless) central Stirling numbers of the first kind.

%H G. C. Greubel, <a href="/A187648/b187648.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = Sum_{k=0..n} A132393(2*k,k).

%F a(n) ~ n^n * c^(2*n) * 2^(3*n-1) / (sqrt(Pi*(c-1)*n) * exp(n) * (2*c-1)^n), where c = -LambertW(-1,-exp(-1/2)/2). - _Vaclav Kotesovec_, May 21 2014

%p seq(add(abs(combinat[stirling1](2*k, k)), k=0..n), n=0..15);

%t Flatten[Table[Sum[Abs[StirlingS1[2k, k]], {k, 0, n}], {n, 0, 15}],1]

%o (Maxima) makelist(sum(abs(stirling1(2*k,k)), k,0,n), n,0,12);

%Y Cf. A132393.

%K nonn,easy

%O 0,2

%A _Emanuele Munarini_, Mar 12 2011