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 A156579 A triangular sequence of the antidiagonal of the backward q squared like factorial: t(n,m)=If[m == 0, n!, Product[Sum[(k - i)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]. 0
 1, 1, 1, 1, 1, 2, 1, 1, 4, 6, 1, 1, 5, 44, 24, 1, 1, 6, 90, 1144, 120, 1, 1, 7, 162, 5220, 65208, 720, 1, 1, 8, 266, 18144, 934380, 7824960, 5040, 1, 1, 9, 408, 51604, 8219232, 507368340, 1932765120, 40320, 1, 1, 10, 594, 126480, 50313900, 14942563776 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row sums are: {1, 2, 4, 12, 75, 1362, 71319, 8782800, 2448445035, 1815296062122, 5172422493520011,...}. Reversed polynomials give this sequence. LINKS FORMULA t(n,m)=If[m == 0, n!, Product[Sum[(k - i)*(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, 4, 6}, {1, 1, 5, 44, 24}, {1, 1, 6, 90, 1144, 120}, {1, 1, 7, 162, 5220, 65208, 720}, {1, 1, 8, 266, 18144, 934380, 7824960, 5040}, {1, 1, 9, 408, 51604, 8219232, 507368340, 1932765120, 40320}, {1, 1, 10, 594, 126480, 50313900, 14942563776, 830054604240, 970248090240, 362880}, {1, 1, 11, 830, 276804, 235885200, 245582145900, 108766921725504, 4080548434443840, 982861315413120, 3628800} MATHEMATICA Clear[t, n, m, i, k, a, b]; t[n_, m_] = If[m == 0, n!, Product[Sum[(k - i)*(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: A307977 A295259 A255009 * A322266 A190284 A327639 Adjacent sequences:  A156576 A156577 A156578 * A156580 A156581 A156582 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 10 2009 STATUS approved

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Last modified April 11 09:24 EDT 2021. Contains 342886 sequences. (Running on oeis4.)