cp's OEIS Frontend

A154108 A000110 / (1,2,3,...): (convolved with (1,2,3,...) = Bell numbers).

%I A154108 #21 Jan 09 2024 16:30:55
%S A154108 1,0,2,7,27,114,523,2589,13744,77821,467767,2972432,19895813,
%T A154108 139824045,1028804338,7905124379,63287544055,526827208698,
%U A154108 4551453462543,40740750631417,377254241891064,3608700264369193,35613444194346451,362161573323083920,3790824599495473121
%N A154108 A000110 / (1,2,3,...): (convolved with (1,2,3,...) = Bell numbers).
%C A154108 This is the sequence which must be convolved with (1,2,3,...), offset 0, to generate the Bell numbers starting (1, 2, 5, 15, 52, ...) offset 1;
%C A154108 equivalent to row sums of triangle A154109 = (1, 2, 5, 15, 52, ...).
%C A154108 A variant of A011965. - _R. J. Mathar_, Jan 07 2009
%F A154108 A000110 / (1,2,3,...); where A000110 (the Bell numbers) begins with offset 1: (1, 2, 5, 15, 52, 203, 877, ...).
%F A154108 G.f.: (A000110(x)-1)*(x-1)^2, where A000110(x) is the g.f. of the Bell numbers. - _R. J. Mathar_, Nov 27 2018
%e A154108 A000110(5) = 52 = (1, 0, 2, 7, 27) convolved with (1, 2, 3, 4, 5) = (5 + 0 + 6 + 14 + 27).
%t A154108 nmax = 30; Table[a[j]/.SolveAlways[Table[Sum[a[k]*(n-k), {k, 0, n}]==BellB[n], {n, 1, nmax+1}], a][[1]], {j, 0, nmax}] (* _Vaclav Kotesovec_, Jul 26 2021 *)
%Y A154108 Cf. A000110, A154109.
%K A154108 nonn
%O A154108 1,3
%A A154108 _Gary W. Adamson_, Jan 04 2009
%E A154108 More terms from _Vaclav Kotesovec_, Jul 26 2021