

A193973


Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n1,x)+n+1 with p(0,x)=1, and q(n,x)=x*p(n1,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
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OFFSET

0,1


COMMENTS

See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.


LINKS

Table of n, a(n) for n=0..69.


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. A193842, A193974.
Sequence in context: A099424 A117955 A074049 * A245057 A127521 A102399
Adjacent sequences: A193970 A193971 A193972 * A193974 A193975 A193976


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 10 2011


STATUS

approved



