A294587 -id:A294587 - cp's OEIS frontend

A294588 Expansion of Product_{k>=1} (1 - k*x^k)^(k^2).

1, -1, -8, -19, -13, 131, 497, 1149, 662, -4780, -22394, -55992, -75053, 44519, 614871, 2048356, 4311107, 4894537, -4917495, -44555890, -140584885, -292542844, -369256294, 110050979, 2247025840, 7757437455, 17600976064, 27240355017, 15747025855, -71354553868

Offset: 0

Seiichi Manyama, Nov 03 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..6653

Column k=2 of A294587.

Cf. A285241.

N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-k*x^k)^k^2))

A294589 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 - j*x^j)^(j^k).

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 1, 1, 5, 6, 1, 1, 9, 14, 14, 1, 1, 17, 36, 42, 25, 1, 1, 33, 98, 140, 103, 56, 1, 1, 65, 276, 498, 481, 289, 97, 1, 1, 129, 794, 1844, 2419, 1774, 690, 198, 1, 1, 257, 2316, 7002, 12745, 12173, 5925, 1771, 354, 1, 1, 513, 6818, 27020, 69283, 89706, 56974, 20076, 4206, 672, 1

Offset: 0

Seiichi Manyama, Nov 03 2017

			Square array begins:
    1,  1,   1,   1,    1, ...
    1,  1,   1,   1,    1, ...
    3,  5,   9,  17,   33, ...
    6, 14,  36,  98,  276, ...
   14, 42, 140, 498, 1844, ...

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Columns k=0..3 give A006906, A266941, A285241, A294590.
Rows n=0-1 give A000012.
Cf. A144048, A294587.

A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k+1+j/d)) * A(n-j,k) for n > 0.

cp's OEIS Frontend

A294588 Expansion of Product_{k>=1} (1 - k*x^k)^(k^2).

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