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A208611
Triangle of coefficients of polynomials v(n,x) jointly generated with A208610; see the Formula section.
3
1, 2, 3, 2, 6, 7, 2, 8, 18, 17, 2, 10, 30, 52, 41, 2, 12, 44, 102, 146, 99, 2, 14, 60, 170, 328, 402, 239, 2, 16, 78, 258, 610, 1014, 1090, 577, 2, 18, 98, 368, 1016, 2076, 3044, 2920, 1393, 2, 20, 120, 502, 1572, 3756, 6792, 8932, 7746, 3363, 2, 22, 144
OFFSET
1,2
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...3
2...6....7
2...8....18...17
2...10...30...52...41
First five polynomials v(n,x):
1
2 + 3x
2 + 6x + 7x^2
2 + 8x + 18x^2 + 17x^3
2 + 10x + 30x^2 + 52x^3 + 41x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A208610 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208611 *)
CROSSREFS
Cf. A208610.
Sequence in context: A348083 A306156 A276125 * A209582 A158279 A153984
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 01 2012
STATUS
approved