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A187652
Alternated binomial cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).
0
1, 0, 10, 194, 5932, 237624, 11820780, 702992968, 48662470640, 3843811669088, 341207224961856, 33627579102171680, 3643463136559851440, 430456189350273371648, 55075003474909952394848, 7586546772496980353804704
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*s(2*k,k).
a(n) ~ c * d^n * (n-1)!, where d = 8*w^2/(2*w-1), where w = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... and c = 0.11686978539934159049334861225275481804523808136863346883911376048... - Vaclav Kotesovec, Jul 05 2021
MAPLE
seq(sum((-1)^(n-k)*binomial(n, k)*abs(combinat[stirling1](2*k, k)), k=0..n), n=0..12);
MATHEMATICA
Table[Sum[(-1)^(n - k)Binomial[n, k]Abs[StirlingS1[2k, k]], {k, 0, n}], {n, 0, 15}]
PROG
(Maxima) makelist(sum((-1)^(n-k)*binomial(n, k)*abs(stirling1(2*k, k)), k, 0, n), n, 0, 12);
CROSSREFS
Cf. A187646.
Sequence in context: A006436 A252974 A341503 * A361311 A007816 A365176
KEYWORD
nonn,easy,changed
AUTHOR
Emanuele Munarini, Mar 12 2011
STATUS
approved