A323632 Stirling transform of Jacobsthal numbers (A001045).

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

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..558

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

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

Sequence in context: A335868 A126033 A369622 * A369265 A369297 A256672

Adjacent sequences: A323629 A323630 A323631 * A323633 A323634 A323635

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 21 2019

Status

approved