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 A193891 Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=x^n+2x^(n-1)+3x^(n-2)+...+nx+(n+1). 2
 1, 1, 2, 2, 5, 8, 3, 8, 14, 20, 4, 11, 20, 30, 40, 5, 14, 26, 40, 55, 70, 6, 17, 32, 50, 70, 91, 112, 7, 20, 38, 60, 85, 112, 140, 168, 8, 23, 44, 70, 100, 133, 168, 204, 240, 9, 26, 50, 80, 115, 154, 196, 240, 285, 330, 10, 29, 56, 90, 130, 175, 224, 276, 330 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..8000 EXAMPLE First six rows: 1 1...2 2...5....8 3...8....14...20 4...11...20...30...40 5...14...26...40...55...70 MATHEMATICA z = 9; p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1; q[n_, x_] := p[n, x]; t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0; w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1 g[n_] := CoefficientList[w[n, x], {x}] TableForm[Table[Reverse[g[n]], {n, -1, z}]] Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193891 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]]  (* A193892 *) PROG (Haskell) a193891 n k = a193891_tabl !! n !! k a193891_row n = a193891_tabl !! n a193891_tabl = [1] : map fst (iterate    (\(xs, i) -> (zipWith (+) (0:xs) [i, 2 * i ..], i + 1)) ([1, 2], 2)) -- Reinhard Zumkeller, Nov 10 2013 CROSSREFS Cf. A193722, A193892. Sequence in context: A254746 A011021 A077232 * A193906 A224791 A210637 Adjacent sequences:  A193888 A193889 A193890 * A193892 A193893 A193894 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 08 2011 STATUS approved

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Last modified September 28 00:46 EDT 2021. Contains 347698 sequences. (Running on oeis4.)