A193963 Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{((k+1)^2)*x^k : 0<=k<=n}.

1, 4, 1, 9, 20, 5, 16, 45, 56, 14, 25, 80, 126, 120, 30, 36, 125, 224, 270, 220, 55, 49, 180, 350, 480, 495, 364, 91, 64, 245, 504, 750, 880, 819, 560, 140, 81, 320, 686, 1080, 1375, 1456, 1260, 816, 204, 100, 405, 896, 1470, 1980, 2275, 2240, 1836, 1140

Offset

0,2

Comments

See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

Links

Table of n, a(n) for n=0..53.

Example

First six rows:
1
4....1
9....20....5
16...45....56....14
25...80....126...120...30
36...125...224...270...220...55

Mathematica

z = 12;
p[n_, x_] := Sum[((k + 1)^2)*x^k, {k, 0, n}]
q[n_, x_] := p[n, x]
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}]]  (* A193963 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193964 *)

Crossrefs

Cf. A193722, A193964.

Sequence in context: A143763 A278350 A128626 * A028941 A364109 A348180

Adjacent sequences: A193960 A193961 A193962 * A193964 A193965 A193966

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved