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A208613 Triangle of coefficients of polynomials v(n,x) jointly generated with A208612; see the Formula section. 3
1, 3, 2, 5, 7, 3, 7, 17, 16, 5, 9, 34, 51, 33, 8, 11, 60, 127, 129, 65, 13, 13, 97, 272, 386, 302, 124, 21, 15, 147, 525, 975, 1052, 666, 231, 34, 17, 212, 938, 2186, 3049, 2646, 1409, 423, 55, 19, 294, 1578, 4482, 7757, 8650, 6285, 2887, 764, 89, 21 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,...
LINKS
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=(x+1)*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
3...2
5...7....3
7...17...16...3
9...34...51...33...8
First five polynomials v(n,x):
1
3 + 2x
5 + 7x + 3x^2
7 + 17x + 16x^2 + 3x^3
9 + 34x + 51x^2 + 33x^3 + 8x^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] + (x + 1)*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[%] (* A208612 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208613 *)
CROSSREFS
Cf. A208612.
Sequence in context: A128224 A125026 A130295 * A209584 A209140 A265903
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 01 2012
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)