A193979 Triangular array: the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n, with p(0,x)=1.

1, 2, 3, 3, 5, 9, 4, 7, 13, 21, 5, 9, 17, 28, 41, 6, 11, 21, 35, 52, 71, 7, 13, 25, 42, 63, 87, 113, 8, 15, 29, 49, 74, 103, 135, 169, 9, 17, 33, 56, 85, 119, 157, 198, 241, 10, 19, 37, 63, 96, 135, 179, 227, 278, 331, 11, 21, 41, 70, 107, 151, 201, 256, 315, 377

Offset

0,2

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..64.

Example

First six rows:
1
2...3
3...5...9
4...7...13....21
5...9...17....28...41
6...11...21...35...52...71

Mathematica

z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n;
q[n_, x_] := p[n, x];
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}]]  (* A193979 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A193980 *)

Crossrefs

Cf. A193842, A193980.

Sequence in context: A107854 A118808 A265019 * A059503 A317644 A194000

Adjacent sequences: A193976 A193977 A193978 * A193980 A193981 A193982

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved