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A323632 Stirling transform of Jacobsthal numbers (A001045). 0
0, 1, 2, 7, 31, 152, 813, 4741, 29956, 203305, 1470795, 11276718, 91221419, 775677177, 6910797962, 64326920851, 623981351195, 6293426736344, 65867162316433, 714062197266081, 8005397253530924, 92676194887133693, 1106385117766336919, 13603803900252612966, 172082332173918135687 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

FORMULA

E.g.f.: (exp(2*(exp(x) - 1)) - exp(1 - exp(x)))/3.

a(n) = Sum_{k=0..n} Stirling2(n,k)*A001045(k).

a(n) = (A001861(n) - A000587(n))/3.

MATHEMATICA

nmax = 24; CoefficientList[Series[(Exp[2 (Exp[x] - 1)] - Exp[1 - Exp[x]])/3, {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[StirlingS2[n, k] (2^k - (-1)^k)/3, {k, 0, n}], {n, 0, 24}]

Table[(BellB[n, 2] - BellB[n, -1])/3, {n, 0, 24}]

CROSSREFS

Cf. A000587, A001045, A001861, A263575, A263576.

Sequence in context: A055836 A076177 A126033 * A256672 A007863 A302061

Adjacent sequences:  A323629 A323630 A323631 * A323633 A323634 A323635

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 21 2019

STATUS

approved

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Last modified July 17 18:47 EDT 2019. Contains 325109 sequences. (Running on oeis4.)