A155866 A 'Morgan Voyce' transform of the Bell numbers A000110.

1, 2, 6, 22, 91, 413, 2032, 10754, 60832, 365815, 2327835, 15612872, 109992442, 811500784, 6253327841, 50211976959, 419239644142, 3632891419054, 32616077413970, 302915722319509, 2906047810600157, 28761123170398258

Offset

0,2

Comments

Image of Bell numbers under Riordan array (1/(1-x), x/(1-x)^2).

Links

G. C. Greubel, Table of n, a(n) for n = 0..550

Formula

G.f.: 1/(1 -x -x/(1 -x -x/(1 -x -x/(1 -x -2*x/(1 -x -x/(1 -x -3*x/(1 -x -x/(1 -x -4*x/(1 - ... (continued fraction).

a(n) = Sum_{k=0..n} binomial(n+k,2k)*A000110(k).

a(n) = Sum_{k=0..n} A085478(n,k)*A000110(k). - Philippe Deléham, Jan 31 2009

Mathematica

A155866[n_]:= Sum[Binomial[n+j, 2*j]*BellB[j], {j, 0, n}];
Table[A155866[n], {n, 0, 30}] (* G. C. Greubel, Jun 10 2021 *)

Prog

(Magma) [(&+[Binomial(n+j, 2*j)*Bell(j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Jun 10 2021
(Sage)
def A155866(n): return sum( binomial(n+j, 2*j)*bell_number(j) for j in (0..n) )
[A155866(n) for n in (0..30)] # G. C. Greubel, Jun 10 2021

Crossrefs

Cf. A000110, A085478.

Sequence in context: A341382 A107591 A279569 * A150273 A342292 A303923

Adjacent sequences: A155863 A155864 A155865 * A155867 A155868 A155869

Keyword

easy,nonn

Author

Paul Barry, Jan 29 2009

Status

approved