A029761 - OEIS

%I #19 Nov 27 2018 11:37:03

%S 1,3,7,16,40,116,395,1551,6847,33290,175708,996696,6031281,38710303,

%T 262288647,1868825536,13955504572,108907053412,885935408411,

%U 7495705968467,65829634763895,599033379716074,5638952863115576,54830878201599424,549981672834888561

%N Partial sums of A005001.

%C Convolution of A000027 (assuming offset 0) by A000110. - _R. J. Mathar_, Nov 27 2018

%H Alois P. Heinz, <a href="/A029761/b029761.txt">Table of n, a(n) for n = 0..500</a>

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

%p b:= proc(n) option remember; `if`(n>0, b(n-1), 0)+combinat[bell](n) end:

%p a:= proc(n) option remember; `if`(n>0, a(n-1), 0)+b(n) end:

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Apr 20 2012

%t Table[Sum[BellB[k], {k, 0, n }], {n, 0, 24}] // Accumulate (* _Jean-François Alcover_, Mar 13 2014 *)

%Y Cf. A005001.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.