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 1-2 of 2 results.

A365977 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+1) / (5*k+1) ).

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 840, 6720, 60480, 604800, 6652800, 83462400, 1138233600, 16746912000, 264176640000, 4444771968000, 80719172352000, 1556132497920000, 31722198842880000, 681437830993920000, 15378172899747840000, 366025806545817600000
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A296676, A365975, A365976.
Cf. A365969.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+1)/(5*k+1)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/5)} (5*k)! * binomial(n,5*k+1) * a(n-5*k-1).

A365989 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+4) / (5*k+4) ).

Original entry on oeis.org

1, 0, 0, 0, 6, 0, 0, 0, 1260, 40320, 0, 0, 1247400, 172972800, 6227020800, 0, 3405402000, 1235025792000, 153848927232000, 6402373705728000, 19799007228000, 14783258730240000, 4243499220280320000, 545332851008225280000, 25852227123135781368000
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2023

Keywords

Crossrefs

Cf. A365969, A365972, A365974.
Cf. A365895, A365990.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\5, x^(5*k+4)/(5*k+4)))))

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-4)/5)} a(n-5*k-4)/(n-5*k-4)!.
Showing 1-2 of 2 results.

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

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