A014327 Convolution of Bell and Catalan numbers.

1, 2, 5, 14, 43, 143, 512, 1974, 8226, 37224, 183456, 984098, 5719900, 35767592, 238720688, 1688044543, 12568879291, 98065500372, 798734909795, 6771216844711, 59602783525634, 543665320690323, 5129940111134397, 49997388546860666, 502624275694700979

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Formula

From G. C. Greubel, Jan 08 2023: (Start)

a(n) = Sum_{j=0..n} A000110(j)*A000108(n-j).

G.f.: (1/(2*x))*(1 - sqrt(1-4*x))*Sum_{j>=0} A000110(j)*x^j. (End)

Mathematica

A014327[n_]:= A014327[n]= Sum[BellB[j]*CatalanNumber[n-j], {j, 0, n}];
Table[A014327[n], {n, 0, 40}] (* G. C. Greubel, Jan 08 2023 *)

Prog

(Magma)
A014327:= func< n | (&+[Bell(j)*Catalan(n-j): j in [0..n]]) >;
[A014327(n): n in [0..40]]; // G. C. Greubel, Jan 08 2023
(SageMath)
def A014327(n): return sum(bell_number(j)*catalan_number(n-j) for j in range(n+1))
[A014327(n) for n in range(41)] # G. C. Greubel, Jan 08 2023

Crossrefs

Cf. A000108, A000110.

Sequence in context: A202060 A098569 A137549 * A173437 A137550 A047970

Adjacent sequences: A014324 A014325 A014326 * A014328 A014329 A014330

Keyword

nonn

Author

N. J. A. Sloane

Status

approved