A293299 -id:A293299 - cp's OEIS frontend

A293300 E.g.f.: Product_{m>0} 1/(1 + x^m).

1, -1, 0, -6, 24, -120, 720, -5040, 80640, -725760, 7257600, -79833600, 1437004800, -18681062400, 261534873600, -5230697472000, 104613949440000, -1778437140480000, 32011868528640000, -729870602452992000, 17030314057236480000, -408727537373675520000

Offset: 0

Seiichi Manyama, Oct 05 2017

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Seiichi Manyama, Table of n, a(n) for n = 0..446

Column k=1 of A293299.

Cf. A081362.

nn = 30; x = 'x + O('x^nn); Vec(serlaplace(prod(m=1, nn, 1/(1 + x^m )))) \\ Michel Marcus, Oct 05 2017

a(n) = n! * A081362(n).

A293301 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} 1/(Sum_{j=0..k} (-1)^jx^(ji)/j!).

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 1, 4, 0, 1, 1, 3, 18, 0, 1, 1, 3, 12, 120, 0, 1, 1, 3, 13, 66, 840, 0, 1, 1, 3, 13, 74, 450, 7920, 0, 1, 1, 3, 13, 73, 510, 3510, 75600, 0, 1, 1, 3, 13, 73, 500, 4130, 32760, 887040, 0, 1, 1, 3, 13, 73, 501, 4040, 38430, 335160, 10886400, 0, 1, 1, 3

Offset: 0

Seiichi Manyama, Oct 05 2017

			Square array begins:
   1,   1,   1,   1,   1, ...
   0,   1,   1,   1,   1, ...
   0,   4,   3,   3,   3, ...
   0,  18,  12,  13,  13, ...
   0, 120,  66,  74,  73, ...
   0, 840, 450, 510, 500, ...

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

Columns k=0..2 give A000007, A053529, A293302.
Rows n=0 gives A000012.
Main diagonal gives A000262.
Cf. A293135, A293139, A293299.

cp's OEIS Frontend

A293300 E.g.f.: Product_{m>0} 1/(1 + x^m).

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A293301 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} 1/(Sum_{j=0..k} (-1)^jx^(ji)/j!).

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cp's OEIS Frontend

A293300 E.g.f.: Product_{m>0} 1/(1 + x^m).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A293301 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} 1/(Sum_{j=0..k} (-1)^j*x^(j*i)/j!).

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A293301 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} 1/(Sum_{j=0..k} (-1)^jx^(ji)/j!).