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A193971
Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=(x+1)^n.
2
2, 3, 5, 4, 11, 9, 5, 19, 26, 14, 6, 29, 55, 50, 20, 7, 41, 99, 125, 85, 27, 8, 55, 161, 259, 245, 133, 35, 9, 71, 244, 476, 574, 434, 196, 44, 10, 89, 351, 804, 1176, 1134, 714, 276, 54, 11, 109, 485, 1275, 2190, 2562, 2058, 1110, 375, 65, 12, 131, 649, 1925
OFFSET
0,1
COMMENTS
See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.
EXAMPLE
First six rows:
2
3...5
4...11....9
5...19...26...14
6...29...55...50...20
7...41...99...125..85...27
MAPLE
# The function 'fission' is defined in A193842.
p := (n, x) -> `if`(n=0, 1, x*p(n-1, x)+n+1);
q := (n, x) -> (x+1)^n;
A193971_row := n -> fission(p, q, n);
for n from 0 to 5 do A193971_row(n) od; # Peter Luschny, Jul 23 2014
MATHEMATICA
z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
q[n_, x_] := (x + 1)^n
p1[n_, k_] := Coefficient[p[n, x], x^k];
p1[n_, 0] := p[n, x] /. x -> 0;
d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
h[n_] := CoefficientList[d[n, x], {x}]
TableForm[Table[Reverse[h[n]], {n, 0, z}]]
Flatten[Table[Reverse[h[n]], {n, -1, z}]] (* A193971 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]] (* A193972 *)
PROG
(Sage) # uses[fission from A193842]
p = lambda n, x: x*p(n-1, x)+n+1 if n > 0 else 1
q = lambda n, x: (x+1)^n
A193971_row = lambda n: fission(p, q, n);
for n in range(7): A193971_row(n) # Peter Luschny, Jul 23 2014
CROSSREFS
Sequence in context: A213900 A213648 A302849 * A258861 A171038 A023395
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved