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.

A284319 Expansion of Product_{k>=0} (1 - x^(5*k+2)) in powers of x.

Original entry on oeis.org

1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 2, 0, -1, -1, 0, 2, 0, -1, -1, 0, 3, 0, -2, -1, 0, 3, 0, -3, -1, 1, 4, 0, -4, -1, 1, 4, 0, -5, -1, 2, 5, 0, -7, -1, 3, 5, 0, -8, -1, 5, 6, -1, -10, -1, 6, 6, -1, -12, -1, 9, 7, -2, -14, -1, 11, 7, -3
Offset: 0

Views

Author

Seiichi Manyama, Mar 25 2017

Keywords

Crossrefs

Cf. Product_{k>=0} (1 - x^(5*k+m)): A284314 (m=1), this sequence (m=2), A284320 (m=3), A284317 (m=4).
Cf. A281272, A284280.

Programs

  • Mathematica
    CoefficientList[Series[Product[1 - x^(5k + 2), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *)
  • PARI
    Vec(prod(k=0, 100, 1 - x^(5*k + 2)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284280(k)*a(n-k), a(0) = 1.

A374077 Expansion of Product_{k>=1} 1 / (1 + x^(5*k-2)).

Original entry on oeis.org

1, 0, 0, -1, 0, 0, 1, 0, -1, -1, 0, 1, 1, -1, -1, -1, 2, 1, 0, -2, -1, 1, 2, 0, -2, -2, 2, 2, 1, -3, -2, 1, 4, 1, -3, -4, 2, 4, 3, -5, -5, 0, 7, 4, -4, -8, 0, 7, 8, -5, -9, -4, 10, 9, -3, -13, -5, 9, 14, -3, -14, -10, 12, 16, 1, -19, -12, 10, 23, 1, -20, -20, 13, 26, 8, -26
Offset: 0

Views

Author

Ilya Gutkovskiy, Jun 27 2024

Keywords

Crossrefs

Cf. A081360, A081362, A109699, A281271, A284320, A374064, A374065, A374076, A374078, A374079.

Programs

  • Mathematica
    nmax = 75; CoefficientList[Series[Product[1/(1 + x^(5 k - 2)), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = (1/n) Sum[DivisorSum[k, (-1)^(k/#) # &, Mod[#, 5] == 3 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]

A284322 Expansion of Product_{k>=0} (1 - x^(5*k+2))*(1 - x^(5*k+3)) in powers of x.

Original entry on oeis.org

1, 0, -1, -1, 0, 1, 0, -1, -1, 1, 2, 1, -2, -2, 1, 3, 1, -3, -3, 2, 5, 1, -5, -5, 2, 7, 2, -7, -7, 4, 11, 3, -11, -11, 5, 15, 4, -15, -14, 8, 22, 6, -21, -21, 10, 30, 8, -29, -28, 15, 42, 11, -40, -39, 19, 56, 15, -53, -51, 27, 76, 20, -72, -70, 34, 99, 26, -94, -90
Offset: 0

Views

Author

Seiichi Manyama, Mar 25 2017

Keywords

Links

Crossrefs

Cf. A003106, A284152, A284319, A284320, A284321.

Programs

  • Mathematica
    CoefficientList[Series[Product[(1 - x^(5k + 2)) ( 1 - x^(5k + 3)), {k, 0, 100}], {x, 0, 100}],x] (* Indranil Ghosh, Mar 25 2017 *)
  • PARI
    Vec(prod(k=0, 100, (1 - x^(5*k + 2)) * (1 - x^(5*k + 3))) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284152(k)*a(n-k), a(0) = 1.
Showing 1-3 of 3 results.

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

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