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 A156576 A triangular sequence of the antidiagonal of the q squared like factorial: t(n,m)=If[m == 0, n!, Product[Sum[(i + 1)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]. 0
 1, 1, 1, 1, 1, 2, 1, 1, 5, 6, 1, 1, 7, 85, 24, 1, 1, 9, 238, 4165, 120, 1, 1, 11, 513, 33796, 537285, 720, 1, 1, 13, 946, 160569, 18486412, 172468485, 5040, 1, 1, 15, 1573, 554356, 255786417, 37065256060, 132628264965, 40320, 1, 1, 17, 2430, 1549405 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row sums are: {1, 2, 4, 13, 118, 4534, 572327, 191121467, 169949903708, 503243397794904, 7528543001953603041,...}. The q squared binomials turn out rational. Based on polynomials: p(x,n) =(1-x)^2*Sum[(k + 1)*(x)^k, {k, 0, n - 1}]; where: q(x,n)= Sum[(k + 1)*(x)^k, {k, 0, n - 1}]; is a count up polynomial. LINKS FORMULA t(n,m)=If[m == 0, n!, Product[Sum[(i + 1)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]]; out_(n,m)=antidiagonal(t(n,m)) EXAMPLE {1}, {1, 1}, {1, 1, 2}, {1, 1, 5, 6}, {1, 1, 7, 85, 24}, {1, 1, 9, 238, 4165, 120}, {1, 1, 11, 513, 33796, 537285, 720}, {1, 1, 13, 946, 160569, 18486412, 172468485, 5040}, {1, 1, 15, 1573, 554356, 255786417, 37065256060, 132628264965, 40320}, {1, 1, 17, 2430, 1549405, 2057215116, 1979019508329, 263459840074480, 237802479082245, 362880}, {1, 1, 19, 3553, 3727620, 11566308325, 46207108720476, 72054121278750561, 6482165905192505920, 974276756799957765, 3628800} MATHEMATICA Clear[t, n, m, i, k, a, b]; t[n_, m_] = If[m == 0, n!, Product[Sum[(i + 1)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}]; b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}]; Flatten[%] CROSSREFS Sequence in context: A086856 A052916 A326048 * A293219 A266572 A266681 Adjacent sequences:  A156573 A156574 A156575 * A156577 A156578 A156579 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 10 2009 STATUS approved

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Last modified February 21 05:23 EST 2020. Contains 332086 sequences. (Running on oeis4.)