A294586 -id:A294586 - cp's OEIS frontend

A294584 Expansion of Product_{k>=1} (1 - k^2*x^k)^(k^2).

1, -1, -16, -65, -79, 831, 4789, 15099, 6450, -162454, -922222, -2766802, -2885883, 17436735, 123724783, 429826690, 823702295, -482288111, -11124249861, -50746426204, -140257438535, -188609543978, 446818695084, 4049784546745, 15671762002156

Offset: 0

Seiichi Manyama, Nov 03 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..3799

Column k=2 of A294583.

Cf. A294586.

nmax = 30; CoefficientList[Series[Product[(1 - k^2*x^k)^(k^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 12 2017 *)

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

A294585 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^k*x^j)^(j^k).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 17, 14, 5, 1, 1, 65, 98, 42, 7, 1, 1, 257, 794, 514, 103, 11, 1, 1, 1025, 6818, 7194, 2435, 289, 15, 1, 1, 4097, 60074, 107170, 69475, 12752, 690, 22, 1, 1, 16385, 535538, 1649322, 2177411, 715277, 58849, 1771, 30

Offset: 0

Seiichi Manyama, Nov 03 2017

			Square array begins:
   1,  1,   1,    1,      1, ...
   1,  1,   1,    1,      1, ...
   2,  5,  17,   65,    257, ...
   3, 14,  98,  794,   6818, ...
   5, 42, 514, 7194, 107170, ...

Seiichi Manyama, Antidiagonals n = 0..113, flattened

Columns k=0..2 give A000041, A266941, A294586.

Rows n=0-1 give A000012.

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

cp's OEIS Frontend

A294584 Expansion of Product_{k>=1} (1 - k^2*x^k)^(k^2).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI