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.

A327694 Expansion of Product_{k>=1} B(x^k), where B(x) is the g.f. of A284321.

Original entry on oeis.org

1, 0, -1, -1, -1, 1, -1, 0, 0, 1, 4, 2, -1, -2, 1, 2, 0, -5, -2, 0, 5, -1, -6, -7, -3, 6, -1, -2, -6, 7, 18, 7, -8, -6, 1, 12, 4, -10, -7, 6, 27, 10, -21, -25, -1, 19, -4, -29, -26, 11, 39, 6, -27, -42, -3, 40, 12, -45, -32, 28, 90, 24, -55, -57, 9, 75, 14, -57, -59, 57, 139
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2019

Keywords

Crossrefs

Convolution inverse of A327691.
Cf. A284321, A327716.

Formula

G.f.: Product_{i>=1} Product_{j>=1} (1 - x^(i*(5*j-2)))*(1 - x^(i*(5*j-3))).

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 1-2 of 2 results.

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