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 A193787 Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=(x+1)^n and q(n,x)=1+x^n. 1
 1, 1, 1, 1, 1, 2, 1, 2, 1, 4, 1, 3, 3, 1, 8, 1, 4, 6, 4, 1, 16, 1, 5, 10, 10, 5, 1, 32, 1, 6, 15, 20, 15, 6, 1, 64, 1, 7, 21, 35, 35, 21, 7, 1, 128, 1, 8, 28, 56, 70, 56, 28, 8, 1, 256, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 512, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.  A193787 is the mirror (obtained by reversing rows) of A193554. LINKS EXAMPLE First six rows: 1 1....1 1....1....2 1....2....1....4 1....3....3....1...8 1....4....6....4...1...16 (viz., Pascal's triangle with row sum at end of each row) MATHEMATICA z = 12; a = 1; b = 1; p[n_, x_] := (a*x + b)^n q[n_, x_] := 1 + x^n ; q[n_, 0] := q[n, x] /. x -> 0; 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}]]  (* A193787 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]]  (* A193554 *) CROSSREFS Cf. A193722, A193554. Sequence in context: A279186 A164799 A274451 * A072614 A287597 A238552 Adjacent sequences:  A193784 A193785 A193786 * A193788 A193789 A193790 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 05 2011 STATUS approved

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Last modified August 21 05:30 EDT 2019. Contains 326162 sequences. (Running on oeis4.)