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.

A365969 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+1) / (5*k+1) ).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 121, 841, 3361, 10081, 25201, 3684241, 50309281, 369738721, 1926648361, 7980936601, 1335634023361, 27705746752321, 302258931418081, 2283161710263841, 13419441405835201, 2498339829188508481, 70152448708746111961, 1025314852704395518441
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A000246, A193437, A193438.
Cf. A333882, A365977.

Programs

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

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/5)} a(n-5*k-1)/(n-5*k-1)!.
a(0) = a(1) = ... = a(4) = 1; a(n) = a(n-1) + 120 * binomial(n-1,5) * a(n-5).

A365975 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(3*k+1) / (3*k+1) ).

Original entry on oeis.org

1, 1, 2, 6, 30, 180, 1260, 10800, 104760, 1130760, 13776480, 184044960, 2670220080, 42222280320, 718144004160, 13061603808000, 254036916144000, 5247117638294400, 114652672773408000, 2647321293055507200, 64330669872690566400, 1640738743703289331200
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A296676, A365976, A365977.

Programs

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

Formula

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

A365976 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+1) / (4*k+1) ).

Original entry on oeis.org

1, 1, 2, 6, 24, 144, 1008, 8064, 72576, 766080, 8934912, 113895936, 1573254144, 23864924160, 389247344640, 6786673496064, 125855767166976, 2492616008171520, 52243870155079680, 1154797100239749120, 26835102086208159744, 656159502089355264000
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A296676, A365975, A365977.

Programs

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

Formula

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

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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