A292577 -id:A292577 - cp's OEIS frontend

A293387 Expansion of (eta(q^2)^2/(eta(q)eta(q^3)))^2 in powers of q.

1, 2, 1, 4, 6, 2, 12, 16, 5, 28, 36, 12, 60, 76, 24, 120, 150, 46, 228, 280, 86, 416, 504, 152, 732, 878, 262, 1252, 1488, 442, 2088, 2464, 725, 3408, 3996, 1168, 5460, 6364, 1852, 8600, 9972, 2886, 13344, 15400, 4436, 20424, 23472, 6736, 30876, 35346, 10103

Offset: 0

Seiichi Manyama, Oct 07 2017

nonn

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

Cf. A262930, A292577.

nmax = 100; CoefficientList[Series[Product[((1 - x^(2*k))^2/((1 - x^k)*(1 - x^(3*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 08 2017 *)

G.f.: Product_{k>0} ((1 - x^(2*k))^2/((1 - x^k)*(1 - x^(3*k))))^2.

A293388 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} (1 + Sum_{j=1..k} (-1)^jjx^(j*i))^2.

Original entry on oeis.org

1, 1, 0, 1, -2, 0, 1, -2, -1, 0, 1, -2, 3, 2, 0, 1, -2, 3, -2, 1, 0, 1, -2, 3, -8, 1, 2, 0, 1, -2, 3, -8, 7, -6, -2, 0, 1, -2, 3, -8, 15, -6, 14, 0, 0, 1, -2, 3, -8, 15, -14, 17, -20, -2, 0, 1, -2, 3, -8, 15, -24, 17, -14, 22, -2, 0, 1, -2, 3, -8, 15, -24, 27

Offset: 0

Seiichi Manyama, Oct 07 2017

			Square array begins:
   1,  1,  1,  1,   1, ...
   0, -2, -2, -2,  -2, ...
   0, -1,  3,  3,   3, ...
   0,  2, -2, -8,  -8, ...
   0,  1,  1,  7,  15, ...
   0,  2, -6, -6, -14, ...

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

Columns k=0..1 give A000007, A002107.
Rows n=0 gives A000012.
Main diagonal gives A293389.
Product_{i>0} 1/(1 + Sum_{j=1..k} (-1)^j*j*x^(j*i))^m: A292577 (m=-2), A293307 (m=-1), A293305 (m=1), this sequence (m=2).

cp's OEIS Frontend

A293387 Expansion of (eta(q^2)^2/(eta(q)eta(q^3)))^2 in powers of q.

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A293388 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} (1 + Sum_{j=1..k} (-1)^jjx^(j*i))^2.

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cp's OEIS Frontend

A293387 Expansion of (eta(q^2)^2/(eta(q)eta(q^3)))^2 in powers of q.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A293388 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} (1 + Sum_{j=1..k} (-1)^j*j*x^(j*i))^2.

Views

Author

Keywords

Examples

Links

Crossrefs

A293388 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} (1 + Sum_{j=1..k} (-1)^jjx^(j*i))^2.