A193975 Triangular array: the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n+1, where p(0,x)=1.

2, 3, 8, 4, 11, 20, 5, 14, 26, 40, 6, 17, 32, 50, 70, 7, 20, 38, 60, 85, 112, 8, 23, 44, 70, 100, 133, 168, 9, 26, 50, 80, 115, 154, 196, 240, 10, 29, 56, 90, 130, 175, 224, 276, 330, 11, 32, 62, 100, 145, 196, 252, 312, 375, 440, 12, 35, 68, 110, 160, 217, 280

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..61.

Example

First six rows:
2
3...8
4...11...20
5...14...26...40
6...17...32...50...70
7...20...38...60...85...112

Mathematica

z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
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}]]  (* A193975 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A193976 *)

Crossrefs

Cf. A193842, A193976.

Sequence in context: A158928 A198369 A193731 * A224665 A098514 A161198

Adjacent sequences: A193972 A193973 A193974 * A193976 A193977 A193978

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved