A029761 Partial sums of A005001.

1, 3, 7, 16, 40, 116, 395, 1551, 6847, 33290, 175708, 996696, 6031281, 38710303, 262288647, 1868825536, 13955504572, 108907053412, 885935408411, 7495705968467, 65829634763895, 599033379716074, 5638952863115576, 54830878201599424, 549981672834888561

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Convolution of A000027 (assuming offset 0) by A000110. - R. J. Mathar, Nov 27 2018

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A005001.

Programs

Maple

b:= proc(n) option remember; `if`(n>0, b(n-1), 0)+combinat[bell](n) end:
a:= proc(n) option remember; `if`(n>0, a(n-1), 0)+b(n) end:
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 20 2012

Mathematica

Table[Sum[BellB[k], {k, 0, n }], {n, 0, 24}] // Accumulate (* Jean-François Alcover, Mar 13 2014 *)

Formula

G.f.: (1/(1 - x)^2) * Sum_{i>=0} x^i / Product_{j=1..i} (1 - j*x). - Ilya Gutkovskiy, Jun 05 2017