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A193893 Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n}. 2
1, 2, 4, 12, 28, 44, 36, 90, 150, 210, 80, 208, 360, 520, 680, 150, 400, 710, 1050, 1400, 1750, 252, 684, 1236, 1860, 2520, 3192, 3864, 392, 1078, 1974, 3010, 4130, 5292, 6468, 7644, 576, 1600, 2960, 4560, 6320, 8176, 10080, 12000, 13920, 810 (list; table; graph; refs; listen; history; text; internal format)
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..45.

EXAMPLE

First six rows:

1

2....4

12...28....44

36...90....150...210

80...208...360...520....680

150..400...710...1050...1400...1760

MATHEMATICA

z = 9;

p[n_, x_] := Sum[(k + 1) (n + 1)*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}]]  (* A193893 *)

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

Flatten[Table[g[n], {n, -1, z}]]  (* A193894 *)

CROSSREFS

Cf. A193722.

Sequence in context: A148174 A232218 A292065 * A096581 A275434 A151258

Adjacent sequences:  A193890 A193891 A193892 * A193894 A193895 A193896

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

STATUS

approved

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Last modified September 16 18:09 EDT 2021. Contains 347473 sequences. (Running on oeis4.)