A192940 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x)=(x+2)(x+4)...(x+2n).

0, 1, 7, 58, 583, 6959, 96510, 1527125, 27170285, 537109100, 11682187715, 277285358845, 7132907069640, 197684330603485, 5872470327374035, 186153757195641730, 6272161769194950475, 223842624694659656675, 8435226009748039509150

Offset

0,3

Comments

For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232.

Links

Table of n, a(n) for n=0..18.

Formula

Conjecture: a(n) +(-4*n+1)*a(n-1) +(4*n^2-6*n+1)*a(n-2)=0. - R. J. Mathar, May 08 2014

Example

The first four polynomials p(n,x) and their reductions are as follows:
p(0,x)=1
p(1,x)=x+2 -> x+2
p(2,x)=(x+2)(x+4) -> 9+7x
p(3,x)=(x+2)(x+4)(x+6) -> 61+58x
From these, read
A192939=(1,2,9,61,...) and A192940=(0,1,7,58,...)

Mathematica

(See A192939.)

Crossrefs

Cf. A192232, A192744, A192939.

Sequence in context: A163048 A318233 A367321 * A126130 A323254 A123766

Adjacent sequences: A192937 A192938 A192939 * A192941 A192942 A192943

Keyword

nonn

Author

Clark Kimberling, Jul 13 2011

Status

approved