A294260 -id:A294260 - cp's OEIS frontend

A294254 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} (1-x^j) - 1).

1, 1, 0, 1, -1, 0, 1, -1, 1, 0, 1, -1, -1, -1, 0, 1, -1, -1, 11, 1, 0, 1, -1, -1, 5, -23, -1, 0, 1, -1, -1, 5, 25, -101, 1, 0, 1, -1, -1, 5, 1, -41, 991, -1, 0, 1, -1, -1, 5, 1, 199, -1769, -1849, 1, 0, 1, -1, -1, 5, 1, 79, -1409, 7181, -24751, -1, 0, 1, -1, -1, 5

Offset: 0

Seiichi Manyama, Oct 26 2017

			Square array A(n,k) begins:
   1,  1,    1,   1,   1, ...
   0, -1,   -1,  -1,  -1, ...
   0,  1,   -1,  -1,  -1, ...
   0, -1,   11,   5,   5, ...
   0,  1,  -23,  25,   1, ...
   0, -1, -101, -41, 199, ...

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

Columns k=0..5 give A000007, A033999, A294255, A294256, A294257, A294258.
Rows n=0 gives A000012.
Main diagonal gives A294260.
Cf. A294250.

B(j,k) is the coefficient of Product_{i=1..k} (1-x^i).

A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(A000217(k),n)} j*B(j,k)*A(n-j,k)/(n-j)! for n > 0.

A294341 E.g.f.: exp(Sum_{n>=1} A010815(n)*x^n/n).

Original entry on oeis.org

1, -1, 0, 2, -2, 18, -128, 740, -3204, -6076, 210304, -1097064, -29284760, 398231768, 792490752, -124480674448, 1471405254928, -2684728872720, -64686947480576, -626709774748384, -10524779012515104, 689522178752789024, 34910956277827256320

Offset: 0

Seiichi Manyama, Oct 28 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..451

Cf. A294260.

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} A010815(k)*a(n-k)/(n-k)! for n > 0.

cp's OEIS Frontend

A294254 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} (1-x^j) - 1).

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