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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved