A292160 -id:A292160 - cp's OEIS frontend

A292162 Main diagonal of A292160.

0, -1, -2, 24, 60, 245, 642, 1365, 2552, 5094, -92010, -147752, -476940, -1083134, -2645230, -5251515, -10399760, -18340246, -33854778, -56744526, -95736020, 1650319440, 2252563082, 6443314668, 13202694120, 29698078100, 55023636486, 113357565936

Offset: 0

Seiichi Manyama, Sep 10 2017

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Cf. A292161.

A292161(n) + i*a(n) = [x^n] Product_{k>=0} (1 - n*i*x^k), where i is sqrt(-1).

A292140 G.f.: Im((2*i; x)_oo), where (a; q)_oo is the q-Pochhammer symbol, i = sqrt(-1).

Original entry on oeis.org

-2, -2, -2, 6, 6, 14, 22, 30, 38, 54, 30, 46, 30, 14, -34, -74, -154, -226, -362, -498, -698, -762, -1058, -1218, -1474, -1634, -1890, -1914, -2074, -2002, -1962, -1570, -1210, -266, 606, 2190, 3454, 6030, 8382, 11926, 15334, 20190, 24758, 30990, 36678, 44134

Offset: 0

Seiichi Manyama, Sep 09 2017

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Seiichi Manyama, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Column k=2 of A292160.

Cf. A278400, A292135, A292141.

(2*i; x)_oo is the g.f. for A292135(n) + i*a(n).

A292159 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Re((k*i; x)_inf), and (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

Original entry on oeis.org

1, 1, 0, 1, -1, 0, 1, -4, -1, 0, 1, -9, -4, -2, 0, 1, -16, -9, -8, -2, 0, 1, -25, -16, -18, -8, -3, 0, 1, -36, -25, -32, -18, -12, -2, 0, 1, -49, -36, -50, -32, -27, 4, -3, 0, 1, -64, -49, -72, -50, -48, 54, 0, -2, 0, 1, -81, -64, -98, -72, -75, 208, 45, 16, -2

Offset: 0

Seiichi Manyama, Sep 10 2017

			Square array begins:
   1,  1,  1,   1,   1, ...
   0, -1, -4,  -9, -16, ...
   0, -1, -4,  -9, -16, ...
   0, -2, -8, -18, -32, ...
   0, -2, -8, -18, -32, ...

Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Columns k=0..2 give A000007, A278399, A292135.
Rows n=0..1 give A000012, (-1)*A000290.
Main diagonal gives A292161.
Cf. A292160.

cp's OEIS Frontend

A292162 Main diagonal of A292160.

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A292140 G.f.: Im((2*i; x)_oo), where (a; q)_oo is the q-Pochhammer symbol, i = sqrt(-1).

Views

Author

Keywords

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Crossrefs

Formula

A292159 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Re((k*i; x)_inf), and (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

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Crossrefs