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.

A379856 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x.

Original entry on oeis.org

1, 0, 1, -7, 81, -1181, 21373, -462267, 11663137, -336711385, 10955316501, -396815693759, 15840688752529, -691086583866069, 32717602050027469, -1670649590632148611, 91530694441643402817, -5355984871255569700913, 333392838283336197688741
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A379868, A379877, A379909.
Cf. A379858, A379875.

Programs

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

Formula

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

A379910 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^3) + x*A(x).

Original entry on oeis.org

1, 0, 1, -7, 93, -1531, 32053, -805659, 23747545, -803011879, 30657419361, -1304526138895, 61227806142517, -3142500604364811, 175099735351517005, -10526856054032137891, 679212922630849128753, -46816385951481961302991, 3433289231599510254603193
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A379858, A379871, A379911.

Programs

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

Formula

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

A379911 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^3) + x*A(x)^2.

Original entry on oeis.org

1, 0, 1, -4, 53, -656, 11917, -244896, 6080265, -171274240, 5480682041, -195121452032, 7672945614589, -329902678161408, 15405361461450885, -776248476561903616, 41985495698339969681, -2426188309657908936704, 149180887282915274036977, -9725086440331395237937152
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A377859, A379868, A379879.
Cf. A379858, A379871, A379910.

Programs

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

Formula

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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