A293293 -id:A293293 - cp's OEIS frontend

A293307 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/(1 + Sum_{j=1..k} (-1)^jjx^(j*i)).

1, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 0, 3, 0, 1, 1, 0, -1, 5, 0, 1, 1, 0, 2, -1, 7, 0, 1, 1, 0, 2, 5, 3, 11, 0, 1, 1, 0, 2, 1, 3, 3, 15, 0, 1, 1, 0, 2, 1, -5, 0, -1, 22, 0, 1, 1, 0, 2, 1, 0, 0, 11, -8, 30, 0, 1, 1, 0, 2, 1, 0, 10, 7, 25, -8, 42, 0, 1, 1, 0, 2, 1, 0

Offset: 0

Seiichi Manyama, Oct 05 2017

			Square array begins:
   1, 1,  1, 1,  1, ...
   0, 1,  1, 1,  1, ...
   0, 2,  0, 0,  0, ...
   0, 3, -1, 2,  2, ...
   0, 5, -1, 5,  1, ...
   0, 7,  3, 3, -5, ...

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

Columns k=0..2 give A000007, A000041, A293294.
Rows n=0..1 give A000012, A057427.
Main diagonal gives A122792.
Cf. A293293, A293305.

A293285 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=0..k} j!x^(ji)).

Original entry on oeis.org

1, 1, 0, 1, -1, 0, 1, -1, 0, 0, 1, -1, -2, -1, 0, 1, -1, -2, 3, 1, 0, 1, -1, -2, -3, -1, -1, 0, 1, -1, -2, -3, 11, -5, 1, 0, 1, -1, -2, -3, -13, 7, 9, -1, 0, 1, -1, -2, -3, -13, 55, -15, 3, 2, 0, 1, -1, -2, -3, -13, -65, 33, -63, -20, -2, 0, 1, -1, -2, -3, -13, -65

Offset: 0

Seiichi Manyama, Oct 04 2017

			Square array begins:
   1,  1,  1,  1,   1, ...
   0, -1, -1, -1,  -1, ...
   0,  0, -2, -2,  -2, ...
   0, -1,  3, -3,  -3, ...
   0,  1, -1, 11, -13, ...
   0, -1, -5,  7,  55, ...

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

Columns k=0..2 give A000007, A081362, A293287.
Rows n=0..1 give A000012, (-1)*A057427.
Main diagonal gives A293251.
Cf. A293202, A293293.

A293294 G.f.: Product_{m>0} 1/(1 - x^m + 2!x^(2m)).

Original entry on oeis.org

1, 1, 0, -1, -1, 3, 3, -1, -8, -8, 12, 24, 5, -43, -55, 40, 137, 65, -215, -356, 97, 780, 624, -941, -2199, -260, 4052, 4638, -3536, -12861, -5676, 19858, 31449, -8337, -71220, -54243, 87733, 196679, 20733, -372807, -413794, 330731, 1159718, 497517, -1821469

Offset: 0

Seiichi Manyama, Oct 05 2017

sign

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

Column k=2 of A293293.

Cf. A293072.

nn = 50; Vec(prod(m=1, nn, 1/(1 - x^m + 2*x^(2*m))) + O(x^nn)) \\ Michel Marcus, Oct 05 2017

Convolution inverse of A293072.

cp's OEIS Frontend

A293307 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/(1 + Sum_{j=1..k} (-1)^jjx^(j*i)).

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A293285 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=0..k} j!x^(ji)).

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A293294 G.f.: Product_{m>0} 1/(1 - x^m + 2!x^(2m)).

Views

Author

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PARI

Formula

cp's OEIS Frontend

A293307 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/(1 + Sum_{j=1..k} (-1)^j*j*x^(j*i)).

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A293285 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=0..k} j!*x^(j*i)).

Views

Author

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Examples

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Crossrefs

A293294 G.f.: Product_{m>0} 1/(1 - x^m + 2!*x^(2*m)).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A293307 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/(1 + Sum_{j=1..k} (-1)^jjx^(j*i)).

A293285 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=0..k} j!x^(ji)).

A293294 G.f.: Product_{m>0} 1/(1 - x^m + 2!x^(2m)).