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A193961 Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=sum{((k+1)^2)*x^(n-k)  :  0<=k<=n}. 2
1, 1, 4, 4, 17, 40, 9, 40, 98, 184, 16, 73, 184, 354, 584, 25, 116, 298, 584, 979, 1484, 36, 169, 440, 874, 1484, 2275, 3248, 49, 232, 610, 1224, 2099, 3248, 4676, 6384, 64, 305, 808, 1634, 2824, 4403, 6384, 8772, 11568, 81, 388, 1034, 2104, 3659 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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..49.

EXAMPLE

First six rows:

1

1....4

4....17....40

9....40....98....184

16...73....184...354...584

25...116...298...584...979...1484

MATHEMATICA

z = 12;

p[n_, x_] := Sum[((k + 1)^2)*x^(n - 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}]]  (* A193961 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]]  (* A193962 *)

CROSSREFS

Cf. A193722, A193962.

Sequence in context: A117787 A113727 A214141 * A205110 A116561 A086448

Adjacent sequences:  A193958 A193959 A193960 * A193962 A193963 A193964

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified November 18 23:00 EST 2019. Contains 329305 sequences. (Running on oeis4.)