A294607 -id:A294607 - cp's OEIS frontend

A294605 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-jx^j)^(j^(kj)) in powers of x.

1, 1, -1, 1, -1, -2, 1, -1, -8, -1, 1, -1, -32, -73, -1, 1, -1, -128, -2155, -919, 5, 1, -1, -512, -58921, -259477, -13977, 1, 1, -1, -2048, -1593811, -67041751, -48496477, -253640, 13, 1, -1, -8192, -43044673, -17178144301, -152513231553, -13001163543, -5290184, 4

Offset: 0

Seiichi Manyama, Nov 04 2017

			Square array begins:
    1,    1,       1,         1,            1, ...
   -1,   -1,      -1,        -1,           -1, ...
   -2,   -8,     -32,      -128,         -512, ...
   -1,  -73,   -2155,    -58921,     -1593811, ...
   -1, -919, -259477, -67041751, -17178144301, ...

Seiichi Manyama, Antidiagonals n = 0..52, flattened

Columns k=0..2 give A022661, A294606, A294607.
Rows n=0..1 give A000012, (-1)*A000012.
Cf. A283675, A294609.

A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k*d+1+j/d)) * A(n-j,k) for n > 0.

A294611 Expansion of Product_{k>=1} 1/(1 - kx^k)^(k^(2k)).

Original entry on oeis.org

1, 1, 33, 2220, 264908, 49163017, 13120646934, 4762819155533, 2257121941722156, 1353302171994081060, 1001440370811165212942, 896481721940248699989226, 954894511643935287905899347, 1193519554843091905978411389666

Offset: 0

Seiichi Manyama, Nov 04 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..214

Column k=2 of A294609.

Cf. A294607.

nmax = 20; CoefficientList[Series[Product[1/(1 - k*x^k)^(k^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 05 2017 *)

N=20; x='x+O('x^N); Vec(1/prod(k=1, N, (1-k*x^k)^k^(2*k)))

Convolution inverse of A294607.

cp's OEIS Frontend

A294605 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-jx^j)^(j^(kj)) in powers of x.

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A294611 Expansion of Product_{k>=1} 1/(1 - kx^k)^(k^(2k)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

cp's OEIS Frontend

A294605 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j*x^j)^(j^(k*j)) in powers of x.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A294611 Expansion of Product_{k>=1} 1/(1 - k*x^k)^(k^(2*k)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A294605 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-jx^j)^(j^(kj)) in powers of x.

A294611 Expansion of Product_{k>=1} 1/(1 - kx^k)^(k^(2k)).