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A156535
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A recursion triangle sequence:f(q,k)=(1 - (-q)^k)/(1 + q);q=2; e(n,k)= f(q, k)*e(n - 1, k) + (-q)^(k - 1)e(n - 1, k - 1).
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0
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1, 1, 1, 1, -3, 1, 1, 1, -9, 1, 1, -3, -23, 67, 1, 1, 1, -81, -151, 1083, 1, 1, -3, -239, 1403, 9497, -34677, 1, 1, 1, -729, -5103, 126915, 424313, -2219285, 1, 1, -3, -2183, 31347, 1314417, -12971853, -68273223, 284068395, 1, 1, 1, -6561, -139271, 14960139
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Row sums are:
{1, 2, -1, -6, 43, 854, -24017, -1673886, 204166899, 53793882958,...},
I'm not certain I have this recursion right from the R.Parthasarathy paper.
He says these are related to Stirling 2nd numbers.
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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=2;
e(n,k)= f(q, k)*e(n - 1, k) + (-q)^(k - 1)e(n - 1, k - 1).
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EXAMPLE
| {1},
{1, 1},
{1, -3, 1},
{1, 1, -9, 1},
{1, -3, -23, 67, 1},
{1, 1, -81, -151, 1083, 1},
{1, -3, -239, 1403, 9497, -34677, 1},
{1, 1, -729, -5103, 126915, 424313, -2219285, 1},
{1, -3, -2183, 31347, 1314417, -12971853, -68273223, 284068395, 1},
{1, 1, -6561, -139271, 14960139, 230347569, -3765947181, -15406841031, 72721509291, 1}
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MATHEMATICA
| Clear[e, n, k, q];
f[q_, k_] := (1 - (-q)^k)/(1 + q);
q = 2; 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], {k, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A081297 A110180 A005765 * A080214 A185620 A096066
Adjacent sequences: A156532 A156533 A156534 * A156536 A156537 A156538
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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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