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A323632 Stirling transform of Jacobsthal numbers (A001045). 1
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
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.
MAPLE
b:= proc(n, m) option remember;
`if`(n=0, round(2^m/3), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..24); # Alois P. Heinz, Aug 06 2021
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
Sequence in context: A335868 A126033 A369622 * A369265 A369297 A256672
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 21 2019
STATUS
approved

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Last modified July 21 22:27 EDT 2024. Contains 374478 sequences. (Running on oeis4.)