A371379 G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/2) / (1-x))^4.

1, 4, 34, 344, 3859, 46240, 579722, 7511272, 99782617, 1351784792, 18604380884, 259395030992, 3656180724752, 52011780756632, 745799171500502, 10768038899631476, 156414710103922340, 2284233700081510820, 33517461646190624690, 493917761019513208800

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A349333, A371519, A371521, A371522, A371523.

Programs

PARI

a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+3, k)/(5*k+4));

Formula

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

G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A349333.