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

1, 0, 2, 7, 27, 114, 523, 2589, 13744, 77821, 467767, 2972432, 19895813, 139824045, 1028804338, 7905124379, 63287544055, 526827208698, 4551453462543, 40740750631417, 377254241891064, 3608700264369193, 35613444194346451, 362161573323083920, 3790824599495473121

Offset: 1

Author

Gary W. Adamson, Jan 04 2009

Keywords

• nonn

Comments

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;

equivalent to row sums of triangle A154109 = (1, 2, 5, 15, 52, ...).

A variant of A011965. - R. J. Mathar, Jan 07 2009

Examples

			A000110(5) = 52 = (1, 0, 2, 7, 27) convolved with (1, 2, 3, 4, 5) = (5 + 0 + 6 + 14 + 27).
		

Crossrefs

Cf. A000110, A154109.

Programs

Mathematica

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 *)

Formula

A000110 / (1,2,3,...); where A000110 (the Bell numbers) begins with offset 1: (1, 2, 5, 15, 52, 203, 877, ...).

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

Extensions

More terms from Vaclav Kotesovec, Jul 26 2021