A192463 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) = (x+1) * (2x+1) * ... *(nx+1).

0, 1, 5, 29, 217, 1972, 21118, 260301, 3629725, 56486815, 970463065, 18243125340, 372459101520, 8206928319095, 194114174537635, 4905364150059835, 131898098954671115, 3759963420179237480, 113267438410706216450, 3595408176533129846175

Offset

0,3

Comments

The polynomial p(n,x) is defined by recursively by p(n,x)=(nx+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=0..19.

Example

The first four polynomials p(n,x) and their reductions are as follows:
p(0,x) = 1.
p(1,x)=1+x -> 1+x
p(2,x)=(1+x)(1+2x) -> 3+5x
p(3,x)=(1+x)(1+2x)(1+3x) -> 18+29x
p(4,x)=(1+x)(1+2x)(1+3x)(1+4x) -> 134+217x.
From these, read
A192462=(0,1,3,18,134,...) and A192463=(0,1,5,29,217,...)

Mathematica

(See A192462.)

Crossrefs

Cf. A192232, A192462.

Sequence in context: A121143 A027048 A356408 * A243952 A094856 A057623

Adjacent sequences: A192460 A192461 A192462 * A192464 A192465 A192466

Keyword

nonn

Author

Clark Kimberling, Jul 01 2011

Status

approved