A381779 G.f. A(x) satisfies A(x) = (1 + x*A(x)) * C(x*A(x)^3), where C(x) is the g.f. of A000108.

1, 2, 11, 95, 977, 11028, 132029, 1646428, 21155077, 278127359, 3723466202, 50586670945, 695676081162, 9665426437561, 135464096419620, 1912922793362142, 27190770354633287, 388734441118885467, 5586079818959767743, 80638973170989453862, 1168864771263296930809

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(n+2*k+1,n-k)/(n+4*k+1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(n+2*k+1, n-k)/(n+4*k+1));

Crossrefs

Cf. A054727, A381778.

Cf. A000108.

Sequence in context: A236962 A292916 A290586 * A098621 A266834 A131407

Adjacent sequences: A381776 A381777 A381778 * A381780 A381782 A381783

Keyword

nonn,new

Author

Seiichi Manyama, Mar 07 2025

Status

approved