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 A187649 Alternated cumulative sums of the central Stirling numbers of the second kind. 1
 1, 0, 7, 83, 1618, 40907, 1282745, 48046535, 2093717518, 104081678237, 5813503286418, 360468997583868, 24569735593174392, 1825998838660375668, 146956989225714933732, 12732911083544911106268, 1181728606386262922675817 (list; graph; refs; listen; history; text; internal format)
 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: A099668 A240170 A231259 * A053128 A027819 A269895 Adjacent sequences:  A187646 A187647 A187648 * A187650 A187651 A187652 KEYWORD nonn,easy AUTHOR Emanuele Munarini, Mar 12 2011 STATUS approved

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