A293285 -id:A293285 - cp's OEIS frontend

A293293 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} (-1)^jj!x^(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, 5, -1, 7, 0, 1, 1, 0, 5, 11, 3, 11, 0, 1, 1, 0, 5, -13, 3, 3, 15, 0, 1, 1, 0, 5, -13, -45, 15, -1, 22, 0, 1, 1, 0, 5, -13, 75, 15, 77, -8, 30, 0, 1, 1, 0, 5, -13, 75, 255, -91, 76, -8, 42, 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,  5,   5, ...
   0, 5, -1, 11, -13, ...
   0, 7,  3,  3, -45, ...

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 A293259.
Cf. A293071, A293285.

A293287 G.f.: Product_{m>0} 1/(1 + x^m + 2!x^(2m)).

Original entry on oeis.org

1, -1, -2, 3, -1, -5, 9, 3, -20, 16, 20, -54, 19, 89, -123, -56, 287, -181, -383, 748, 37, -1520, 1406, 1619, -4439, 1190, 7768, -10102, -5494, 25673, -14754, -36660, 66367, 7047, -139852, 125785, 153573, -405349, 98671, 712275, -909382, -514965, 2332540, -1303341

Offset: 0

Seiichi Manyama, Oct 04 2017

sign

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

Column k=2 of A293285.

Cf. A293204.

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

Convolution inverse of A293204.

cp's OEIS Frontend

A293293 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} (-1)^jj!x^(j*i)).

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A293287 G.f.: Product_{m>0} 1/(1 + x^m + 2!x^(2m)).

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cp's OEIS Frontend

A293293 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} (-1)^j*j!*x^(j*i)).

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Author

Keywords

Examples

Links

Crossrefs

A293287 G.f.: Product_{m>0} 1/(1 + x^m + 2!*x^(2*m)).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A293293 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} (-1)^jj!x^(j*i)).

A293287 G.f.: Product_{m>0} 1/(1 + x^m + 2!x^(2m)).