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

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = sum((-1)^(n-k)s(2k,k)),k=0..n)

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

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}]

Prog

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

Crossrefs

Cf. A187646, A332928.

Sequence in context: A134069 A137464 A357915 * A357083 A214687 A160074

Adjacent sequences: A187647 A187648 A187649 * A187651 A187652 A187653

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved