login
A192461
Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
2
1, 3, 21, 199, 2406, 35388, 613141, 12228651, 275906565, 6947421085, 193127008800, 5874229869420, 194051905056955, 6918430857234105, 264771876138591195, 10826136459795957685, 471008148256238771970, 21725067991777448569920
OFFSET
1,2
COMMENTS
The polynomial p(n,x) is defined by recursively by p(n,x)=(nx+n-1)*p(n-1,x) with p[0,x]=1. For an introduction to reductions of polynomials by substitutions such as x^2->x+2, see A192232.
EXAMPLE
The first four polynomials p(n,x) and their reductions are as follows:
p(0,x)=x -> x
p(1,x)=x(1+2x) -> 2+3x
p(2,x)=x(1+2x)(2+3x) -> 13+21x
p(3,x)=x(1+2x)(2+3x)(3+4x) -> 123+199x.
From these, read
A192460=(1,2,13,123,...) and A192461=(1,3,21,199,...)
MATHEMATICA
(See A192460.)
CROSSREFS
Sequence in context: A202826 A372155 A212070 * A199682 A348912 A309638
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 01 2011
STATUS
approved