A293489 -id:A293489 - cp's OEIS frontend

A293486 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} Sum_{j=0..k} x^(j(2i-1))/j!.

1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 6, 0, 1, 1, 1, 6, 24, 0, 1, 1, 1, 7, 24, 120, 0, 1, 1, 1, 7, 24, 180, 720, 0, 1, 1, 1, 7, 25, 180, 1080, 5040, 0, 1, 1, 1, 7, 25, 180, 1200, 10080, 80640, 0, 1, 1, 1, 7, 25, 181, 1200, 10080, 90720, 725760, 0, 1, 1, 1, 7, 25

Offset: 0

Seiichi Manyama, Oct 10 2017

			Square array begins:
   1,   1,   1,   1,   1, ...
   0,   1,   1,   1,   1, ...
   0,   0,   1,   1,   1, ...
   0,   6,   6,   7,   7, ...
   0,  24,  24,  24,  25, ...
   0, 120, 180, 180, 180, ...

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

Columns k=0..3 give A000007, A293487, A293488, A293489.
Rows n=0 gives A000012.
Main diagonal gives A088009.
Cf. A293135.

A293463 Expansion of Product_{m>0} (1 + x^(2m-1) + 2x^(4m-2) + 3x^(6*m-3)).

Original entry on oeis.org

1, 1, 2, 4, 1, 3, 6, 5, 9, 13, 12, 17, 23, 22, 25, 30, 46, 53, 62, 74, 80, 106, 117, 135, 170, 183, 224, 267, 279, 325, 397, 444, 512, 610, 679, 791, 877, 989, 1157, 1298, 1476, 1669, 1909, 2134, 2390, 2721, 3012, 3391, 3887, 4308, 4808, 5460, 6018, 6752, 7552

Offset: 0

Seiichi Manyama, Oct 09 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..500

Column k=3 of A293461.

Cf. A293489.

nmax = 100; CoefficientList[Series[Product[(1 + x^(2*k-1) + 2*x^(4*k-2) + 3*x^(6*k-3)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 09 2017 *)

m = 80; Vec(prod(k=1, m, 1 + x^(2*k-1) + 2*x^(4*k-2) + 3*x^(6*k-3)) + O(x^m)) \\ Michel Marcus, Oct 10 2017

cp's OEIS Frontend

A293486 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} Sum_{j=0..k} x^(j(2i-1))/j!.

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A293463 Expansion of Product_{m>0} (1 + x^(2m-1) + 2x^(4m-2) + 3x^(6*m-3)).

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cp's OEIS Frontend

A293486 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} Sum_{j=0..k} x^(j*(2*i-1))/j!.

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Author

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A293463 Expansion of Product_{m>0} (1 + x^(2*m-1) + 2*x^(4*m-2) + 3*x^(6*m-3)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A293486 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} Sum_{j=0..k} x^(j(2i-1))/j!.

A293463 Expansion of Product_{m>0} (1 + x^(2m-1) + 2x^(4m-2) + 3x^(6*m-3)).