login
A207621
Triangle of coefficients of polynomials v(n,x) jointly generated with A207620; see the Formula section.
3
1, 2, 2, 3, 6, 2, 4, 13, 10, 2, 5, 24, 31, 14, 2, 6, 40, 76, 57, 18, 2, 7, 62, 161, 176, 91, 22, 2, 8, 91, 308, 456, 340, 133, 26, 2, 9, 128, 546, 1044, 1045, 584, 183, 30, 2, 10, 174, 912, 2178, 2794, 2080, 924, 241, 34, 2, 11, 230, 1452, 4224, 6721, 6370
OFFSET
1,2
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...6...2
4...13...10...2
5...24...31...14...2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A207620 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207621 *)
CROSSREFS
Cf. A207620.
Sequence in context: A248164 A338993 A210222 * A209157 A284785 A076333
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved