A193846 Triangular array: the fission of ((x+2)^n) by ((x+1)^n).
2, 4, 8, 8, 28, 26, 16, 80, 136, 80, 32, 208, 512, 568, 242, 64, 512, 1648, 2672, 2188, 728, 128, 1216, 4832, 10288, 12392, 8020, 2186, 256, 2816, 13312, 35072, 55648, 53216, 28432, 6560, 512, 6400, 35072, 110080, 216512, 273376, 216512, 98416
Offset: 0
Examples
First six rows: 2 4....8 8....28....26 16...80....136....80 32...208...512....568....242 64...512...1648...2672...2188...728
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
Programs
-
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 *) -
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
Formula
G.f.: A(x,y) = 2/(1 - 2*(1 + 2*y)*x + y*(2 + 3*y)*x^2). - Andrew Howroyd, Feb 18 2024
Comments