A364987 -id:A364987 - cp's OEIS frontend

A365011 E.g.f. satisfies A(x) = 1 + xexp(-x)A(x)^4.

1, 1, 6, 87, 1964, 60325, 2349114, 110922091, 6159510552, 393373489257, 28407518470070, 2289019332293551, 203608076603605860, 19816972252710998989, 2094926215725519979698, 239037380421621120397395, 29281119335188021375533104, 3832665229749097186190010193

Offset: 0

Seiichi Manyama, Aug 15 2023

nonn

Cf. A295239, A302397, A365010.

Cf. A002293, A364987.

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

a(n) = n! * Sum_{k=0..n} (-k)^(n-k) * A002293(k)/(n-k)!.

A377577 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x)^2)^2.

Original entry on oeis.org

1, 2, 22, 426, 12344, 480010, 23500812, 1389576230, 96382531408, 7675512189714, 690344499939860, 69220070789605582, 7656687699685355256, 926243380308839330426, 121653259759077599227612, 17240419344948437264399670, 2622300119032920100004726432, 426102385668766701871015106338

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A364987, A377576.

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364987.

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

cp's OEIS Frontend

A365011 E.g.f. satisfies A(x) = 1 + xexp(-x)A(x)^4.

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A377577 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x)^2)^2.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A365011 E.g.f. satisfies A(x) = 1 + x*exp(-x)*A(x)^4.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A377577 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x)^2)^2.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A365011 E.g.f. satisfies A(x) = 1 + xexp(-x)A(x)^4.