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

1,3

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

Links

Table of n, a(n) for n=1..25.

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

Example

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

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 *)

Crossrefs

Cf. A000110, A154109.

Sequence in context: A127897 A180473 A011965 * A150629 A150630 A150631

Adjacent sequences: A154105 A154106 A154107 * A154109 A154110 A154111

Keyword

nonn

Author

Gary W. Adamson, Jan 04 2009

Extensions

More terms from Vaclav Kotesovec, Jul 26 2021

Status

approved