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

0,2

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

Formula

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

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 *)

Crossrefs

Cf. A005001.

Sequence in context: A263316 A001698 A261236 * A009337 A323776 A036567

Adjacent sequences: A029758 A029759 A029760 * A029762 A029763 A029764

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved