A292141 -id:A292141 - cp's OEIS frontend

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

-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

sign

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).

A292143 Triangle read by rows: T(n,k) = (-4)^(1 - k mod 2) * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

Original entry on oeis.org

1, 0, 1, 0, 1, 0, 1, -4, 0, 1, -4, 0, 1, -8, 0, 1, -8, -4, 0, 1, -12, -4, 0, 1, -12, -8, 0, 1, -16, -12, 0, 1, -16, -16, 16, 0, 1, -20, -20, 16, 0, 1, -20, -28, 32, 0, 1, -24, -32, 48, 0, 1, -24, -40, 80, 0, 1, -28, -48, 96, 16, 0, 1, -28, -56, 144, 16, 0, 1, -32

Offset: 0

Seiichi Manyama, Sep 09 2017

			First few rows are:
  1;
  0, 1;
  0, 1;
  0, 1,  -4;
  0, 1,  -4;
  0, 1,  -8;
  0, 1,  -8,  -4;
  0, 1, -12,  -4;
  0, 1, -12,  -8;
  0, 1, -16, -12;
  0, 1, -16, -16, 16.

Seiichi Manyama, Rows n = 0..481, flattened

Row sums give A292141.
Columns 0-1 give A000007, A000012.
Cf. A292049.

cp's OEIS Frontend

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

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