A292159 -id:A292159 - cp's OEIS frontend

A292161 Main diagonal of A292159.

1, -1, -4, -18, -32, -75, 1188, 2205, 7936, 19278, 49500, 87120, 185760, 312988, 574868, -10481175, -15271936, -46022672, -98470404, -230150496, -440484000, -932930208, -1572331596, -2940575576, -4940815104, -8508211250, -13542949524, -22406625648

Offset: 0

Seiichi Manyama, Sep 10 2017

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Cf. A292159, A292162.

a(n) + i*A292162(n) = [x^n] Product_{k>=0} (1 - n*i*x^k), where i is sqrt(-1).

A292135 G.f.: Re((2*i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

Original entry on oeis.org

1, -4, -4, -8, -8, -12, 4, 0, 16, 28, 60, 72, 120, 148, 212, 192, 272, 268, 316, 264, 264, 116, 84, -176, -368, -788, -1140, -1848, -2168, -3164, -3884, -5040, -5920, -7412, -8308, -9960, -10872, -12540, -13276, -14768, -14752, -15620, -14644, -14120, -11304

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 A292159.

Cf. A278399, A292140, A292142.

(2*i; x)_inf is the g.f. for a(n) + i*A292140(n).

A292160 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Im((k*i; x)_inf), and (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

Original entry on oeis.org

0, -1, 0, -2, -1, 0, -3, -2, -1, 0, -4, -3, -2, 0, 0, -5, -4, -3, 6, 0, 0, -6, -5, -4, 24, 6, 1, 0, -7, -6, -5, 60, 24, 14, 2, 0, -8, -7, -6, 120, 60, 51, 22, 3, 0, -9, -8, -7, 210, 120, 124, 78, 30, 4, 0, -10, -9, -8, 336, 210, 245, 188, 105, 38, 6, 0, -11, -10

Offset: 0

Seiichi Manyama, Sep 10 2017

			Square array begins:
   0, -1, -2, -3, -4, ...
   0, -1, -2, -3, -4, ...
   0, -1, -2, -3, -4, ...
   0,  0,  6, 24, 60, ...
   0,  0,  6, 24, 60, ...

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

Columns k=0..2 give A000004, A278400, A292140.
Rows 0+2 give (-1)*A001477.
Main diagonal gives A292162.
Cf. A292159.

cp's OEIS Frontend

A292161 Main diagonal of A292159.

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A292135 G.f.: Re((2*i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

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Formula

A292160 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Im((k*i; x)_inf), and (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

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