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A192463 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) = (x+1) * (2x+1) * ... *(nx+1). 2
0, 1, 5, 29, 217, 1972, 21118, 260301, 3629725, 56486815, 970463065, 18243125340, 372459101520, 8206928319095, 194114174537635, 4905364150059835, 131898098954671115, 3759963420179237480, 113267438410706216450, 3595408176533129846175 (list; graph; refs; listen; history; text; internal format)
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: A091124 A121143 A027048 * A243952 A094856 A057623

Adjacent sequences:  A192460 A192461 A192462 * A192464 A192465 A192466

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 01 2011

STATUS

approved

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Last modified September 16 23:53 EDT 2021. Contains 347477 sequences. (Running on oeis4.)