A292131 -id:A292131 - cp's OEIS frontend

A292132 Main diagonal of A292131.

1, -1, -2, 6, 12, 45, -150, -203, -840, -1872, 6390, 8580, 30084, 69108, 165802, -494565, -514320, -1997296, -4202298, -10175526, -18908420, 49930440, 54032770, 190735688, 405256872, 948210600, 1751280726, 3624555168, -7676955468, -6724059944, -26741354430

Offset: 0

Seiichi Manyama, Sep 09 2017

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Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A124577, A291698, A292131.

{a(n) = polcoeff(prod(k=1, n, 1-n*x^k+x*O(x^n)), n)}

a(n) = [x^n] Product_{k=1..n} (1 - n*x^k).

A292128 Expansion of Product_{k>=1} (1 - 3*x^k).

Original entry on oeis.org

1, -3, -3, 6, 6, 15, -12, -3, -30, -48, 6, -12, 15, 78, 186, -21, 168, 42, 42, -246, -408, -156, -399, -552, -498, -246, 213, 1248, -318, 1608, 1392, 2508, 1482, 2976, -480, -1011, 1500, -1704, -4296, -4206, -8499, -8652, -7626, -7050, -192, -13008, -480, -2118

Offset: 0

Seiichi Manyama, Sep 09 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Column k=3 of A292131.
Product_{k>=1} (1 - m*x^k): A010815 (m=1), A070877 (m=2), this sequence (m=3).
Cf. A032308, A242587, A292130.

N=66; x='x+O('x^N); Vec(prod(n=1, N, 1-3*x^n))

G.f.: Sum_{i>=0} (-3)^i*x^(i*(i+1)/2)/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 13 2018

cp's OEIS Frontend

A292132 Main diagonal of A292131.

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