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 A193899 Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=x*p(n-1,x)+2^n, p(0,x)=1. 2
 1, 1, 2, 2, 5, 10, 4, 10, 21, 42, 8, 20, 42, 85, 170, 16, 40, 84, 170, 341, 682, 32, 80, 168, 340, 682, 1365, 2730, 64, 160, 336, 680, 1364, 2730, 5461, 10922, 128, 320, 672, 1360, 2728, 5460, 10922, 21845, 43690, 256, 640, 1344, 2720, 5456, 10920 (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 EXAMPLE First six rows of A193897: 1 1....2 2....5....10 4....10...21...42 8....20...42...85....170 16...40...84...170...341...682 MATHEMATICA z = 12; p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 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}]]  (* A193899 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]]  (* A193900 *) CROSSREFS Cf. A193722, A193900. Sequence in context: A110182 A309867 A304584 * A334017 A208567 A273968 Adjacent sequences:  A193896 A193897 A193898 * A193900 A193901 A193902 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 08 2011 STATUS approved

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Last modified December 9 08:17 EST 2021. Contains 349627 sequences. (Running on oeis4.)