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.

A321361 Expansion of Product_{1 <= i <= j <= k} (1 - x^(i*j*k)).

Original entry on oeis.org

1, -1, -1, 0, -1, 2, 0, 2, -1, 0, 3, -1, -2, -1, 1, -6, 0, -1, -1, 0, 6, 1, 1, 0, 4, 0, 0, 10, -2, -1, -9, 7, -11, 13, -15, -7, -3, -9, 0, 6, -3, -9, 14, -9, 20, -17, 20, -2, 20, 1, 25, -9, 14, 13, -3, -7, -21, -9, -11, 6, -54, 39, -22, -30, -10, 35, -21, 8, -41, -23
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2018

Keywords

Links

Crossrefs

Convolution inverse of A321360.
Cf. A034836, A319359, A321299, A321359.

Formula

G.f.: Product_{k>0} (1 - x^k)^A034836(k).

A321377 Expansion of Product_{1 < i <= j} (1 - x^(i*j)).

Original entry on oeis.org

1, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, -1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 3, 0, 2, -1, 1, 0, 1, -1, -2, -2, -3, 0, -3, -4, -3, -4, -6, 1, -6, -1, -4, -2, 0, 0, -2, 2, 1, 1, 1, 6, 5, 6, 8, 7, 8, 8, 9, 9, 9, 8, 11, 0, 6, 6, 7, 3, 6, -10, 1, -7, -6, -7, -6, -18, -10, -21, -13, -14
Offset: 0

Views

Author

Seiichi Manyama, Nov 08 2018

Keywords

Links

Crossrefs

Convolution inverse of A182270.
Cf. A038548, A211857, A321299, A321376.

Formula

G.f.: Product_{k>0} (1 - x^k)^(A038548(k) - 1).

A321300 Expansion of Product_{1 <= i < j} (1 - x^(i*j)).

Original entry on oeis.org

1, 0, -1, -1, -1, 0, -1, 1, 1, 2, 2, 2, 0, 0, 2, -2, -1, -3, -1, -4, -4, -4, -1, -1, -2, 0, 3, 7, 3, 4, 5, 7, 5, 8, 3, 2, 4, 1, -6, -2, -8, -8, -12, -9, -9, -11, -13, -12, -6, -8, -6, -8, 11, 5, 6, 8, 18, 12, 22, 21, 28, 26, 28, 12, 21, 22, 11, 0, 0, -4, -18, -17, -38
Offset: 0

Views

Author

Seiichi Manyama, Nov 03 2018

Keywords

Links

Crossrefs

Convolution inverse of A321285.
Cf. A056924, A321286, A321299.

Programs

  • Mathematica
    nmax = 100; CoefficientList[Series[Product[(1 - x^k)^Floor[DivisorSigma[0, k]/2], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 03 2018 *)

Formula

G.f.: Product_{k>0} (1 - x^k)^A056924(k).

A319517 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} (1 - x^(i_1*i_2*i_3*i_4)).

Original entry on oeis.org

1, -1, -1, 0, -1, 2, 0, 2, -1, 0, 3, -1, -2, -1, 1, -6, -1, 0, 0, 0, 7, -1, 1, -2, 4, 1, -2, 11, 1, -2, -10, 11, -11, 15, -16, -6, -7, -10, -1, 10, -5, -10, 12, -20, 19, -16, 24, -2, 28, -9, 41, -6, 15, 20, 4, -21, -15, -13, -14, 13, -73, 67, -30, -44, -19, 31, -30
Offset: 0

Views

Author

Seiichi Manyama, Nov 14 2018

Keywords

Links

Crossrefs

Convolution inverse of A321566.
Product_{1 <= i_1 <= i_2 <= ... <= i_b} (1 - x^(i_1 * i_2 * ... * i_b)): A010815 (b=1), A321299 (b=2), A321361 (b=3), this sequence (b=4).
Cf. A218320, A321460, A321567.

Formula

G.f.: Product_{k>0} (1 - x^k)^A218320(k).
Showing 1-4 of 4 results.

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

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