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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
OFFSET
0,3
COMMENTS
See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
LINKS
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
Sequence in context: A254746 A011021 A077232 * A193906 A224791 A210637
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved