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 1-4 of 4 results.

A363357 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))).

Original entry on oeis.org

1, 1, 7, 85, 1581, 39501, 1244953, 47426373, 2120506489, 108894505753, 6317267871501, 408637512353049, 29164082035045477, 2276557391070945477, 192956160476285907457, 17647873882378895267821, 1732445579330211460781937, 181694902682241512454842673
Offset: 0

Views

Author

Seiichi Manyama, Aug 17 2023

Keywords

Crossrefs

Programs

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

Formula

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

A363479 E.g.f. satisfies A(x) = exp(x * A(x)^3 * (1 + x * A(x)^3)).

Original entry on oeis.org

1, 1, 9, 160, 4381, 162816, 7663669, 437164288, 29317265625, 2260685099008, 197088986941921, 19170218777296896, 2058199476739788661, 241779221463040000000, 30847476924400409437389, 4247859315849037948911616, 627960846411135123552180529
Offset: 0

Views

Author

Seiichi Manyama, Aug 17 2023

Keywords

Crossrefs

Programs

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

Formula

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

A365057 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x/2 * A(x)^2)).

Original entry on oeis.org

1, 1, 6, 70, 1242, 29766, 901108, 33007500, 1419955260, 70189326748, 3920638941576, 244244850932424, 16790688671875000, 1262666306235233160, 103110586277262570672, 9086730135842989237456, 859557307380692050631952, 86872483166310571406250000
Offset: 0

Views

Author

Seiichi Manyama, Aug 19 2023

Keywords

Crossrefs

Programs

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

Formula

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