cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A363356 E.g.f. satisfies A(x) = exp(x * A(x) * (1 + x * A(x)^3)).

Original entry on oeis.org

1, 1, 5, 52, 821, 17536, 473497, 15476224, 594230345, 26221431808, 1307680266221, 72739285725184, 4465197522732157, 299855584017743872, 21867349264346912705, 1721013285639521959936, 145394112130209844644113, 13123788855563296766427136
Offset: 0

Views

Author

Seiichi Manyama, Aug 17 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sum(k=0, n, (3*n-2*k+1)^(k-1)*binomial(k, n-k)/k!);

Formula

a(n) = n! * Sum_{k=0..n} (3*n-2*k+1)^(k-1) * binomial(k,n-k)/k!.

A372178 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) * (1 + x * A(x)) ).

Original entry on oeis.org

1, 2, 12, 122, 1800, 35002, 848236, 24664362, 837602352, 32558200370, 1426118691924, 69522324440098, 3733960438696648, 219101400537409002, 13946923555466389884, 957297896801470079258, 70483467144263313405024, 5541471459106022647303522
Offset: 0

Views

Author

Seiichi Manyama, Apr 21 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A363355.
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!.

A372182 E.g.f. A(x) satisfies A(x) = exp( x * A(x)^5 * (1 + x * A(x)^2) ).

Original entry on oeis.org

1, 1, 13, 334, 13329, 724316, 49939411, 4177202562, 411049275265, 46530896718520, 5957142774561531, 851104158600401366, 134246582420467536289, 23171656877102178017028, 4344395473350526080895843, 879206880413471231912831626, 191028062860784640128743389441
Offset: 0

Views

Author

Seiichi Manyama, Apr 21 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n, r=1, s=1, t=5, u=2) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(s*k, n-k)/k!);

Formula

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!.
Showing 1-3 of 3 results.