A187650 Alternated cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).

1, 0, 11, 214, 6555, 262770, 13076765, 777866388, 53853263165, 4254252038764, 377667803463431, 37222867283396314, 4033161189724173207, 476511397553009371918, 60969023704806106263737, 8398605422371512041566888

Offset: 0

Author

Emanuele Munarini, Mar 12 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A187646, A332928.

Programs

Maple

seq(sum((-1)^(n-k)*abs(combinat[stirling1](2*k,k)),k=0..n),n=0..12);

Mathematica

Table[Sum[(-1)^(n-k)Abs[StirlingS1[2k, k]], {k, 0, n}], {n, 0, 15}]

Maxima

makelist(sum((-1)^(n-k)*abs(stirling1(2*k,k)),k,0,n),n,0,12);

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k)*s(2*k,k).

a(n) ~ 2^(3*n-1) * c^(2*n) * n^(n - 1/2) / (sqrt(Pi*(c-1)) * (2*c-1)^n * exp(n)), where c = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... - Vaclav Kotesovec, Jul 05 2021