A364472 G.f. satisfies A(x) = 1 + x*A(x) + x^2*A(x)^6.

1, 1, 2, 8, 35, 163, 808, 4162, 22041, 119325, 657384, 3673394, 20769983, 118610807, 683131766, 3963486380, 23144000681, 135911263309, 802143851323, 4755506884495, 28306896506651, 169110331570307, 1013643450123455, 6094125091837335, 36739933169338731

Offset: 0

Author

Seiichi Manyama, Jul 26 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000045, A000108, A001006, A182454, A186996, A364476.

Cf. A002295.

Programs

PARI

a(n) = sum(k=0, n\2, binomial(n+4*k, k)*binomial(n+3*k, n-2*k)/(5*k+1));

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(n+4*k,k) * binomial(n+3*k,n-2*k) / (5*k+1) = Sum_{k=0..floor(n/2)} binomial(n+4*k,6*k) * binomial(6*k,k) / (5*k+1).