OFFSET
0,1
COMMENTS
See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
FORMULA
G.f.: A(x,y) = 2/(1 - 2*(1 + 2*y)*x + y*(2 + 3*y)*x^2). - Andrew Howroyd, Feb 18 2024
EXAMPLE
First six rows:
2
4....8
8....28....26
16...80....136....80
32...208...512....568....242
64...512...1648...2672...2188...728
MATHEMATICA
p[n_, x_] := (x + 2)^n;
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}]] (* A193846 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]] (* A193847 *)
TableForm[Table[Reverse[h[n]/2], {n, 0, z}]]
Flatten[Table[Reverse[h[n]]/2, {n, -1, z}]] (* A193848 *)
TableForm[Table[h[n]/2, {n, 0, z}]]
Flatten[Table[h[n]/2, {n, -1, z}]] (* A193849 *)
PROG
(PARI) T(n)={[2*Vecrev(p) | p<-Vec(1/(1 - 2*(1 + 2*y)*x + y*(2 + 3*y)*x^2) + O(x*x^n))]}
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Feb 18 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 07 2011
STATUS
approved