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.

A363358 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x)^2)).

Original entry on oeis.org

1, 1, 7, 91, 1809, 48521, 1643863, 67381875, 3243606817, 179405231761, 11213025902631, 781604862035339, 60120379931640625, 5058593367221610009, 462199816484860893559, 45574025454771003821731, 4823543138131670132557377, 545448517762149418525390625
Offset: 0

Views

Author

Seiichi Manyama, Aug 17 2023

Keywords

Crossrefs

Programs

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

Formula

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

A365033 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))^2).

Original entry on oeis.org

1, 1, 9, 127, 2769, 80861, 2976733, 132394011, 6909143265, 414041227417, 28025981914581, 2115049310887679, 176095675272002929, 16035108243371426613, 1585349332849711046829, 169128107565128349122851, 19365426435579375683158977, 2368882573995841615546652081
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(2*k, n-k)/k!);

Formula

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

A365034 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))^3).

Original entry on oeis.org

1, 1, 11, 175, 4317, 142561, 5929513, 297901899, 17557448681, 1188110627137, 90804918357261, 7737033497254579, 727253150819898541, 74760871323339663489, 8344094871249960257009, 1004872166403751985971291, 129883465213311163328142417
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(3*k, n-k)/k!);

Formula

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