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 A141611 A symmetrical triangle of coefficients read by rows: t(n,m)=(n - m + 1)*(m + 1)*binomial[n, m]. 5
 1, 2, 2, 3, 8, 3, 4, 18, 18, 4, 5, 32, 54, 32, 5, 6, 50, 120, 120, 50, 6, 7, 72, 225, 320, 225, 72, 7, 8, 98, 378, 700, 700, 378, 98, 8, 9, 128, 588, 1344, 1750, 1344, 588, 128, 9, 10, 162, 864, 2352, 3780, 3780, 2352, 864, 162, 10, 11, 200, 1215, 3840, 7350, 9072, 7350 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums: [1, 4, 14, 44, 128, 352, 928, 2368, 5888, 14336, 34304, ...] = A007466. Read as a square array, this array factorizes as M*transpose(M), where M = (k*binomial(n,k))n,k>=1 = A003506(n,k). - Peter Bala, Mar 06 2017 LINKS FORMULA O.g.f. (1 - (1 + t)*x + 2*t*x^2)/(1 - (1 + t)*x)^3 = 1 + (2 + 2*t)*x + (3 + 8*t + 3*t^2)*x^2 + (4 + 18*t + 18*t^2 + 4*t^3)*x^3 + .... - Peter Bala, Mar 06 2017 EXAMPLE {1}, {2, 2}, {3, 8, 3}, {4, 18, 18, 4}, {5, 32, 54, 32, 5}, {6, 50, 120, 120, 50, 6}, {7, 72, 225, 320, 225, 72, 7}, {8, 98, 378, 700, 700, 378, 98, 8}, {9, 128, 588, 1344, 1750, 1344, 588, 128, 9}, {10, 162, 864, 2352, 3780, 3780, 2352, 864, 162, 10}, {11, 200, 1215, 3840, 7350, 9072, 7350, 3840, 1215, 200, 11} ... From Peter Bala, Mar 06 2017: (Start) Factorization as a square array   /1         \ /1  2  3  4...\ /1  2   3   4...\   |2  2      | |   2  6 12...| |2  8  12  32...|   |3  6  3   |*|      3 12...|=|3 18  54 120...|   |4 12 12 4 | |         4...| |4 32 120 320...|   |...       | |             | |...            | (End) MATHEMATICA t[n_, m_] := (n - m + 1)*(m + 1)*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] PROG (PARI) t(n, m)=(n - m + 1)*(m + 1)*binomial(n, m) \\ Charles R Greathouse IV, Feb 15 2017 CROSSREFS A007466 (row sums). Cf. A003506. Sequence in context: A295943 A296804 A296952 * A234357 A145596 A186753 Adjacent sequences:  A141608 A141609 A141610 * A141612 A141613 A141614 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula and Gary W. Adamson, Aug 22 2008 STATUS approved

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Last modified April 9 17:32 EDT 2020. Contains 333361 sequences. (Running on oeis4.)