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.

A379876 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)) + x*A(x)^3.

Original entry on oeis.org

1, 0, 1, 5, 53, 689, 11509, 231083, 5448841, 147483665, 4508952641, 153682778435, 5778729641629, 237643665397241, 10610714800698349, 511207317411929339, 26434273616510818961, 1460296693254659368481, 85832214445015447832569, 5348490494660467991798003
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A379871, A379877, A379878.
Cf. A377859, A379875.

Programs

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

Formula

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

A379858 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^3) + x.

Original entry on oeis.org

1, 0, 1, -10, 157, -3136, 77509, -2288896, 78824953, -3105906688, 137925180361, -6818997285376, 371578940493589, -22130352562929664, 1430368670554859533, -99722125119137591296, 7459992570265962997489, -596072767690463855509504, 50666927756525446827810961
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A379871, A379910, A379911.
Cf. A379856, A379875.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (-3*n+4*k-1)^(n-k) * binomial(3*n-3*k+1,k)/( (3*n-3*k+1)*(n-k)! ).

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)! ).
Showing 1-3 of 3 results.

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

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