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A192940
Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x)=(x+2)(x+4)...(x+2n).
2
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 13 2011
STATUS
approved