A371517 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^4.

1, 4, 26, 188, 1459, 11892, 100444, 871528, 7722557, 69590628, 635807180, 5876094308, 54836925779, 516029817620, 4891147100886, 46653935716492, 447490869463145, 4313492172957396, 41763413498670702, 405968522259130636, 3960526930400038404

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A045868, A371516, A371520, A371521.

Cf. A349331, A371483, A371518.

Cf. A371486.

Programs

PARI

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

Formula

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

G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A349331.