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 A178658 Triangle T(n,k) read by rows: the coefficient [x^k] of the series (1-x)^(2n-1)*Sum_{l>=0} A001263(n+3*l,3*l+1)*x^l, in row n>=1 with exponents k>=0. 0
 1, 1, 7, 1, 1, 45, 96, 20, 1, 168, 1316, 1730, 420, 10, 1, 481, 9486, 35959, 35959, 9486, 481, 1, 1, 1165, 48103, 395692, 974863, 816025, 226765, 17248, 196, 1, 2507, 193830, 2977338, 14467635, 26621385, 19654740, 5661084, 558168, 13496, 28, 1, 4935 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums are 1, 9, 162, 3645, 91854, 2480058, 70150212, 2051893701, 61556811030, 1883638417518,.... LINKS FORMULA Let A(n,m) = A001263(n+m,m+1), then T(n,k) = [x^k] (1-x)^(2n-1) * Sum_{l>=0} A(n,3l) *x^l. If n == 2 (mod 3), then T(n,k) = T(n,5(n-2)/3+2-k). EXAMPLE 1; 1, 7, 1; 1, 45, 96, 20; 1, 168, 1316, 1730, 420, 10; 1, 481, 9486, 35959, 35959, 9486, 481, 1; 1, 1165, 48103, 395692, 974863, 816025, 226765, 17248, 196; 1, 2507, 193830, 2977338, 14467635, 26621385, 19654740, 5661084, 558168, 13496, 28; 1, 4935, 662019, 17287475, 146146455, 494277453, 735137025, 494277453, 146146455, 17287475, 662019, 4935, 1; 1, 9058, 1993006, 82927275, 1124706060, 6284964498, 16252722579, 20538756768, 12843595065, 3874383980, 524761304, 27575207, 415404, 825; MATHEMATICA p[x_, n_] = (1 - x)^(2*n - 1)*Sum[(Binomial[3*k + n, 3* k] Binomial[3*k + n, 1 + 3*k]/(3*k + n))*x^k, {k, 0, Infinity}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}]; Flatten[%] CROSSREFS Cf. A001263, A034839 Sequence in context: A166973 A157156 A022170 * A156602 A203389 A174689 Adjacent sequences:  A178655 A178656 A178657 * A178659 A178660 A178661 KEYWORD nonn,tabf AUTHOR Roger L. Bagula, Jun 01 2010 EXTENSIONS Edited by R. J. Mathar, May 13 2016 STATUS approved

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Last modified March 31 16:44 EDT 2020. Contains 333151 sequences. (Running on oeis4.)