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 A156538 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)) 0
 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; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are: 2, 4, -6, -58, 1576, 130734, -31406038, -23016536336, 50226264655566, 329827987437639830,.... LINKS R. Parthasarathy, q-Fermionic Numbers and Their Roles in Some Physical Problems, arXiv:quant-ph/0403216 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)) 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} 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[%] CROSSREFS Sequence in context: A058787 A085056 A265447 * A249768 A217503 A165466 Adjacent sequences:  A156535 A156536 A156537 * A156539 A156540 A156541 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 09 2009 STATUS approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)