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A155866
A 'Morgan Voyce' transform of the Bell numbers A000110.
1
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
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
Sequence in context: A341382 A107591 A279569 * A150273 A342292 A303923
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 29 2009
STATUS
approved