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.

A365897 Expansion of e.g.f. exp( Sum_{k>=0} x^(3*k+5) / (3*k+5)! ).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 126, 1, 0, 1287, 1, 126126, 10803, 1, 5513508, 87210, 488864377, 175388031, 698820, 61841343565, 5037240879, 5194678451481, 5281277511511, 139251621015, 1519441856106345, 387880753064806, 123382468421090541
Offset: 0

Views

Author

Seiichi Manyama, Sep 22 2023

Keywords

Links

Crossrefs

Cf. A057814, A365896, A365898.

Programs

  • PARI
    my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\3, x^(3*k+5)/(3*k+5)!))))

Formula

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

A365898 Expansion of e.g.f. exp( Sum_{k>=0} x^(4*k+5) / (4*k+5)! ).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 126, 0, 0, 1, 2002, 126126, 0, 1, 32878, 11639628, 488864376, 1, 523754, 962159506, 164910249504, 5194672859377, 8390630, 79198593760, 44919303188760, 4895979169961881, 123378675217248882, 6434084214390, 11762691848427520
Offset: 0

Views

Author

Seiichi Manyama, Sep 22 2023

Keywords

Links

Crossrefs

Cf. A057814, A365896, A365897.

Programs

  • PARI
    my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\4, x^(4*k+5)/(4*k+5)!))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/4)} binomial(n-1,4*k+4) * a(n-4*k-5).
E.g.f.: exp( -x + (sinh(x) + sin(x))/2 ).

A365915 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(2*k+5) / (2*k+5)! ).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 252, 1, 1584, 1, 7436, 756757, 31616, 14702689, 129404, 189559657, 11733266992, 2062481617, 516242875084, 20611819933, 14135172627712, 623557476714481, 312148517693820, 52096977907924561, 6121122865591920
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Links

Crossrefs

Cf. A245790, A365916, A365917.
Cf. A006154, A332258.
Cf. A365896.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x+x^3/6-sinh(x))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/2)} binomial(n,2*k+5) * a(n-2*k-5).
E.g.f.: 1 / ( 1 + x + x^3/6 - sinh(x) ).
Showing 1-3 of 3 results.

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

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