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A192459 Coefficient of x in the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments. 2
1, 3, 17, 133, 1315, 15675, 218505, 3485685, 62607195, 1250116875, 27468111825, 658579954725, 17109329512275, 478744992200475, 14354443912433625, 459128747151199125, 15604187119787140875, 561558837528374560875, 21332903166207470462625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The polynomial p(n,x) is defined by recursively by p(n,x)=(x+2n)*p(n-1,x) with p[0,x]=x.  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..18.

FORMULA

a(n) = (1/3)*(2^(n+1)*(n+1)! + (2n-1)!!). - Vaclav Potocek, Feb 04 2016

EXAMPLE

The first four polynomials p(n,x) and their reductions are as follows:

p(0,x)=x -> x

p(1,x)=x(2+x) -> 2+3x

p(2,x)=x(2+x)(4+x) -> 14+17x

p(3,x)=x(2+x)(4+x)(6+x) -> 118+133x.

From these, read

A192457=(1,2,14,118,...) and A192459=(1,3,17,133,...)

MATHEMATICA

(See A192457.)

CROSSREFS

Cf. A192232, A192457.

Sequence in context: A305819 A163684 A093986 * A055214 A105630 A199138

Adjacent sequences:  A192456 A192457 A192458 * A192460 A192461 A192462

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 01 2011

STATUS

approved

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Last modified September 26 23:32 EDT 2020. Contains 337378 sequences. (Running on oeis4.)