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 A193973 Triangular array:  the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=x*p(n-1,x)+1 with p(0,x)=1. 2
 2, 3, 5, 4, 7, 9, 5, 9, 12, 14, 6, 11, 15, 18, 20, 7, 13, 18, 22, 25, 27, 8, 15, 21, 26, 30, 33, 35, 9, 17, 24, 30, 35, 39, 42, 44, 10, 19, 27, 34, 40, 45, 49, 52, 54, 11, 21, 30, 38, 45, 51, 56, 60, 63, 65, 12, 23, 33, 42, 50, 57, 63, 68, 72, 75, 77, 13, 25, 36, 46 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A193842 for the definition of fission of two sequences of polynomials or triangular arrays. This array show the differences of the sequence of triangular numbers A000217); viz., row n consists of t(n) - t(n-k) for k=1..n-1. - Clark Kimberling, Apr 15 2017 LINKS Clark Kimberling, Table of n, a(n) for n = 0..10000 EXAMPLE First six rows: 2 3...5 4...7....9 5...9...12..14 6...11..15..18..20 7...13..18..22..25..27 MATHEMATICA z = 13; p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1; q[0, x_] := 1; q[n_, x_] := x*q[n - 1, x] + 1; p1[n_, k_] := Coefficient[p[n, x], x^k]; p1[n_, 0] := p[n, x] /. x -> 0; d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}] h[n_] := CoefficientList[d[n, x], {x}] TableForm[Table[Reverse[h[n]], {n, 0, z}]] Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193973 *) TableForm[Table[h[n], {n, 0, z}]] Flatten[Table[h[n], {n, -1, z}]]  (* A193974 *) CROSSREFS Cf. A193664, A193842, A193974. Sequence in context: A117955 A074049 A326777 * A245057 A127521 A102399 Adjacent sequences:  A193970 A193971 A193972 * A193974 A193975 A193976 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 10 2011 STATUS approved

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Last modified November 28 00:12 EST 2021. Contains 349395 sequences. (Running on oeis4.)