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.

A365979 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+2) / (5*k+2) ).

Original entry on oeis.org

1, 0, 1, 0, 6, 0, 90, 720, 2520, 51840, 113400, 4276800, 47401200, 444787200, 9725086800, 58378320000, 2029897584000, 30450131712000, 475261239024000, 11952610750080000, 127796530736160000, 4683810971473920000, 90707397988727520000, 1964217505623310080000
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A226226, A365978.
Cf. A365909.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+2)/(5*k+2)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-2)/5)} (5*k+1)! * binomial(n,5*k+2) * a(n-5*k-2).

A365971 Expansion of e.g.f. exp( Sum_{k>=0} x^(3*k+2) / (3*k+2) ).

Original entry on oeis.org

1, 0, 1, 0, 3, 24, 15, 504, 5145, 9072, 300321, 3795120, 12284811, 441965160, 6672128463, 33017539464, 1306646813745, 22946632267104, 156924556846785, 6810382180903392, 136393286581031571, 1209571612450077240, 57211108821810731151, 1286884543482633415320
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A000166, A365972.
Cf. A365978.

Programs

  • Mathematica
    nmax = 20; CoefficientList[Series[(1 + x + x^2)^(1/6) / (E^(ArcTan[Sqrt[3]*x/(2 + x)]/Sqrt[3]) * (1-x)^(1/3)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 30 2024 *)
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\3, x^(3*k+2)/(3*k+2)))))

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-2)/3)} a(n-3*k-2)/(n-3*k-2)!.
Showing 1-2 of 2 results.

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

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