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

Author

Ilya Gutkovskiy, Jan 21 2019

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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}]

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.