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.

A365974 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+3) / (5*k+3) ).

Original entry on oeis.org

1, 0, 0, 2, 0, 0, 40, 0, 5040, 2240, 0, 1663200, 246400, 479001600, 605404800, 44844800, 699941088000, 274450176000, 355699625881600, 836634972096000, 156436600320000, 1437392253237248000, 1021561084051200000, 1124111547465274368000
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A038205, A130915, A365973.
Cf. A365982.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\5, x^(5*k+3)/(5*k+3)))))

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-3)/5)} a(n-5*k-3)/(n-5*k-3)!.

A365981 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+3) / (4*k+3) ).

Original entry on oeis.org

1, 0, 0, 2, 0, 0, 80, 720, 0, 13440, 345600, 3628800, 5913600, 296524800, 7062681600, 92559667200, 442810368000, 18037334016000, 459627769036800, 7475081822208000, 65867064606720000, 2634706112643072000, 74102151110787072000, 1464478283948359680000
Offset: 0

Views

Author

Seiichi Manyama, Sep 24 2023

Keywords

Crossrefs

Cf. A355284, A365980, A365982.
Cf. A365911.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\4, x^(4*k+3)/(4*k+3)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/4)} (4*k+2)! * binomial(n,4*k+3) * a(n-4*k-3).

A365980 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(2*k+3) / (2*k+3) ).

Original entry on oeis.org

1, 0, 0, 2, 0, 24, 80, 720, 5376, 53760, 490752, 6289920, 68766720, 1024607232, 13520332800, 226177695744, 3498759290880, 65257155624960, 1153246338220032, 23793010526453760, 472374431008948224, 10686755493583257600, 235406405307208826880
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A355284, A365981, A365982.
Cf. A130915, A296676.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-atanh(x))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/2)} (2*k+2)! * binomial(n,2*k+3) * a(n-2*k-3).
E.g.f.: 1 / ( 1 + x - arctanh(x) ).

A365990 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+4) / (5*k+4) ).

Original entry on oeis.org

1, 0, 0, 0, 6, 0, 0, 0, 2520, 40320, 0, 0, 7484400, 345945600, 6227020800, 0, 81729648000, 7410154752000, 307697854464000, 6402373705728000, 2375880867360000, 354798209525760000, 25460995321681920000, 1090665702016450560000, 26003493399464380800000
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2023

Keywords

Crossrefs

Cf. A365977, A365979, A365982.
Cf. A365914, A365989.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+4)/(5*k+4)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-4)/5)} (5*k+3)! * binomial(n,5*k+4) * a(n-5*k-4).
Showing 1-4 of 4 results.

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

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