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A193891 Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=x^n+2x^(n-1)+3x^(n-2)+...+nx+(n+1). 2
1, 1, 2, 2, 5, 8, 3, 8, 14, 20, 4, 11, 20, 30, 40, 5, 14, 26, 40, 55, 70, 6, 17, 32, 50, 70, 91, 112, 7, 20, 38, 60, 85, 112, 140, 168, 8, 23, 44, 70, 100, 133, 168, 204, 240, 9, 26, 50, 80, 115, 154, 196, 240, 285, 330, 10, 29, 56, 90, 130, 175, 224, 276, 330 (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

Reinhard Zumkeller, Table of n, a(n) for n = 0..8000

EXAMPLE

First six rows:

1

1...2

2...5....8

3...8....14...20

4...11...20...30...40

5...14...26...40...55...70

MATHEMATICA

z = 9;

p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;

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}]]  (* A193891 *)

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

Flatten[Table[g[n], {n, -1, z}]]  (* A193892 *)

PROG

(Haskell)

a193891 n k = a193891_tabl !! n !! k

a193891_row n = a193891_tabl !! n

a193891_tabl = [1] : map fst (iterate

   (\(xs, i) -> (zipWith (+) (0:xs) [i, 2 * i ..], i + 1)) ([1, 2], 2))

-- Reinhard Zumkeller, Nov 10 2013

CROSSREFS

Cf. A193722, A193892.

Sequence in context: A254746 A011021 A077232 * A193906 A224791 A210637

Adjacent sequences:  A193888 A193889 A193890 * A193892 A193893 A193894

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

STATUS

approved

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Last modified August 13 22:57 EDT 2020. Contains 336473 sequences. (Running on oeis4.)