A070859 Expansion of (1+x*C^4)*C, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 2, 7, 25, 89, 317, 1133, 4069, 14690, 53312, 194446, 712538, 2622437, 9690475, 35941065, 133756845, 499349550, 1869614340, 7018807650, 26415146190, 99642310170, 376674137034, 1426776136770, 5414477628770, 20583342248324, 78376598475952, 298899265388444

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

From Seiichi Manyama, Nov 24 2025: (Start)

a(n) = 3 * (7*n^3+13*n^2+12*n+8) * (2*n)!/(n! * (n+4)!).

a(n) = binomial(2*n,n) + 5*binomial(2*n,n-2)/(n+3) - binomial(2*n,n-4). (End)

Prog

(PARI) a(n) = 3*(7*n^3+13*n^2+12*n+8)*(2*n)!/(n!*(n+4)!); \\ Seiichi Manyama, Nov 24 2025

Crossrefs

Cf. A000108, A000344, A026012.

Sequence in context: A030017 A131430 A007484 * A048576 A018907 A052936

Adjacent sequences: A070856 A070857 A070858 * A070860 A070861 A070862

Keyword

nonn

Author

N. J. A. Sloane, Jun 06 2002

Status

approved