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 A177938 Triangle T(n,k) = (-1)^(k+n)*A054655(n,n-k), 0<=k
 1, 1, 1, 6, 5, 1, 60, 47, 12, 1, 840, 638, 179, 22, 1, 15120, 11274, 3325, 485, 35, 1, 332640, 245004, 74524, 11985, 1075, 51, 1, 8648640, 6314664, 1961470, 336049, 34300, 2086, 70, 1, 259459200, 188204400, 59354028, 10630508, 1182769, 83720 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS An unsigned, row-reversed variant of A054655. Row sums are apparently A001813(n). LINKS FORMULA Row generating function: Gamma(x+2n)/Gamma(x+n) = sum_{k>=0) T(n,k)*x^k. EXAMPLE 1; 1, 1; 6, 5, 1; 60, 47, 12, 1; 840, 638, 179, 22, 1; 15120, 11274, 3325, 485, 35, 1; 332640, 245004, 74524, 11985, 1075, 51, 1; 8648640, 6314664, 1961470, 336049, 34300, 2086, 70, 1; 259459200, 188204400, 59354028, 10630508, 1182769, 83720, 3682, 92, 1; 8821612800, 6366517200, 2030997852, 375923456, 44493813, 3492489, 181818, 6054, 117, 1; 335221286400, 240947474400, 77559615576, 14724404900, 1825849430, 154530705, 9040773, 361050, 9420, 145, 1; MATHEMATICA Clear[p, x, n, m, f, l] p[x_, n_] = If[n == 0, 1, (n - 1)!/Beta[x + n, n]]; f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m]]; l[n_] := Length[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]]; Table[Table[FullSimplify[ExpandAll[f[n, m]]], {m, 1, l[n]}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A177824 A197517 A102079 * A112282 A098866 A144689 Adjacent sequences:  A177935 A177936 A177937 * A177939 A177940 A177941 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, May 15 2010 STATUS approved

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