cp's OEIS Frontend

A029761 Partial sums of A005001.

%I A029761 #21 Jul 08 2025 19:19:55
%S A029761 1,3,7,16,40,116,395,1551,6847,33290,175708,996696,6031281,38710303,
%T A029761 262288647,1868825536,13955504572,108907053412,885935408411,
%U A029761 7495705968467,65829634763895,599033379716074,5638952863115576,54830878201599424,549981672834888561
%N A029761 Partial sums of A005001.
%C A029761 Convolution of A000027 (assuming offset 0) by A000110. - _R. J. Mathar_, Nov 27 2018
%H A029761 Alois P. Heinz, <a href="/A029761/b029761.txt">Table of n, a(n) for n = 0..500</a>
%F A029761 G.f.: (1/(1 - x)^2) * Sum_{i>=0} x^i / Product_{j=1..i} (1 - j*x). - _Ilya Gutkovskiy_, Jun 05 2017
%p A029761 b:= proc(n) option remember; `if`(n>0, b(n-1), 0)+combinat[bell](n) end:
%p A029761 a:= proc(n) option remember; `if`(n>0, a(n-1), 0)+b(n) end:
%p A029761 seq(a(n), n=0..30);  # _Alois P. Heinz_, Apr 20 2012
%t A029761 Table[Sum[BellB[k], {k, 0, n }], {n, 0, 24}] // Accumulate (* _Jean-François Alcover_, Mar 13 2014 *)
%Y A029761 Cf. A005001.
%K A029761 nonn
%O A029761 0,2
%A A029761 _N. J. A. Sloane_