A192461 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.

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.

Links

Table of n, a(n) for n=1..18.

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

Cf. A192232, A192460.

Sequence in context: A202826 A372155 A212070 * A199682 A348912 A309638

Adjacent sequences: A192458 A192459 A192460 * A192462 A192463 A192464

Keyword

nonn

Author

Clark Kimberling, Jul 01 2011

Status

approved