A372200 -id:A372200 - cp's OEIS frontend

A372201 E.g.f. A(x) satisfies A(x) = exp( 3 * x / (1 - x * A(x)^(1/3))^3 ).

1, 3, 27, 351, 6309, 145143, 4083669, 136159299, 5256248265, 230783968395, 11364265672929, 620524946670687, 37222254648712989, 2433741005377774719, 172301622840992025117, 13133140607475128862747, 1072406955985984437773841, 93406430850089038192704915

Offset: 0

Seiichi Manyama, Apr 21 2024

nonn

Cf. A161630, A372200.

Cf. A364938.

a(n, r=3, s=3, t=0, u=1) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);

E.g.f.: A(x) = B(x)^3 where B(x) is the e.g.f. of A364938.

If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.

A372202 E.g.f. A(x) satisfies A(x) = exp( 2 * x * (1 + x * A(x)^(1/2))^2 ).

Original entry on oeis.org

1, 2, 12, 92, 1024, 14192, 241624, 4855832, 112887520, 2981919392, 88274138344, 2896196131688, 104341759873168, 4096112838853232, 174063938788299928, 7961816811743462648, 390072804802178286016, 20381525361707872355648, 1131437006755346662551496

Offset: 0

Seiichi Manyama, Apr 21 2024

nonn

Cf. A363744, A372200.

a(n, r=2, s=2, t=0, u=1) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(s*k, n-k)/k!);

E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A363744.

If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(s*k,n-k)/k!.

cp's OEIS Frontend

A372201 E.g.f. A(x) satisfies A(x) = exp( 3 * x / (1 - x * A(x)^(1/3))^3 ).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula