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A156538
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A recursion triangle sequence:f(q,k)=(1 - (-q)^k)/(1 + q);q=3; e(n,k)= f(q, k)*e(n - 1, k) + (-q)^(k - 1)e(n - 1, k - 1); t(n,m)=(e(n, k) + e(n, n - k + 1))
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0
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2, 2, 2, 2, -10, 2, 2, -31, -31, 2, 2, 989, -406, 989, 2, 2, 81578, -16213, -16213, 81578, 2, 2, -19816168, 3777869, 670556, 3777869, -19816168, 2, 2, -14445938413, 2685823244, 251846999, 251846999, 2685823244, -14445938413, 2, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are:
{2, 4, -6, -58, 1576, 130734, -31406038, -23016536336, 50226264655566,
329827987437639830,...}.
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REFERENCES
| R.Parthasarathy,q-Fermionic Numbers and Their Roles in Some Physical Problems: http://arxiv.org/abs/quant-ph/0403216
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FORMULA
| f(q,k)=(1 - (-q)^k)/(1 + q);q=3;
e(n,k)= f(q, k)*e(n - 1, k) + (-q)^(k - 1)e(n - 1, k - 1);
t(n,m)=(e(n, k) + e(n, n - k + 1))
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EXAMPLE
| {2},
{2, 2},
{2, -10, 2},
{2, -31, -31, 2},
{2, 989, -406, 989, 2},
{2, 81578, -16213, -16213, 81578, 2},
{2, -19816168, 3777869, 670556, 3777869, -19816168, 2},
{2, -14445938413, 2685823244, 251846999, 251846999, 2685823244, -14445938413, 2},
{2, 31593267585083, -5943908538085, -551461074016, 30468709598, -551461074016, -5943908538085, 31593267585083, 2},
{2, 207283428627421172, -38813632028151640, -3653430427397491, 97627546947872, 97627546947872, -3653430427397491, -38813632028151640, 207283428627421172, 2}
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MATHEMATICA
| Clear[e, n, k, q]; f[q_, k_] := (1 - (-q)^k)/(1 + q); |Q q = 3; e[n_, 0] := 0;
e[n_, 1] := 1'
e[n_, n_] := 1; e[n_, k_] := 0 /; k >= n + 1;
e[n_, k_] := f[q, k]*e[n - 1, k] + (-q)^(k - 1)e[n - 1, k - 1];
Table[Table[(e[n, k] + e[n, n - k + 1]), {k, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A152660 A058787 A085056 * A165466 A175392 A112727
Adjacent sequences: A156535 A156536 A156537 * A156539 A156540 A156541
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 09 2009
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