A187649 Alternated cumulative sums of the central Stirling numbers of the second kind.

1, 0, 7, 83, 1618, 40907, 1282745, 48046535, 2093717518, 104081678237, 5813503286418, 360468997583868, 24569735593174392, 1825998838660375668, 146956989225714933732, 12732911083544911106268, 1181728606386262922675817

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..345

Formula

Formula: a(n) = sum((-1)^(n-k)S(2k,k)),k=0..n)

Maple

seq(sum((-1)^(n-k)*combinat[stirling2](2*k, k), k=0..n), n=0..12);
# Alternative:
L:= [seq((-1)^n*Stirling2(2*n, n), n=0..50)]:
P:= ListTools:-PartialSums(L):
seq((-1)^(n+1)*P[n], n=1..51); # Robert Israel, Aug 25 2017

Mathematica

Table[Sum[(-1)^(n-k)StirlingS2[2k, k], {k, 0, n}], {n, 0, 16}]

Prog

(Maxima) makelist(sum((-1)^(n-k)*stirling2(2*k, k), k, 0, n), n, 0, 12);

Crossrefs

Cf. A008277 (Stirling2 triangle)

Sequence in context: A348303 A240170 A231259 * A368853 A316377 A053128

Adjacent sequences: A187646 A187647 A187648 * A187650 A187651 A187652

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved