A185965 Central coefficients of number triangle A185962.

1, -2, 0, 8, -10, -30, 98, 40, -648, 680, 3058, -8712, -6760, 65674, -52710, -348128, 856358, 1011330, -7116754, 3891920, 41214978, -87043088, -143941360, 793389048, -224365750, -4961373872, 8914590594, 19893652520, -89559777800, 540262170, 601349934194, -905363401312, -2693832315240, 10150582469480, 2943320005570, -73015796693016, 89846661676688

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Formula

a(n)=A185962(2n,n); a(n)=sum{i=0..2n+2, C(2n+2,i)*sum{C(n+j,j)*C(j,n-i-j)*(-1)^(n-j)}}.

Conjecture: 15*n*(n-1)*a(n) +10*(2*n-1)*(n-1)*a(n-1) +(109*n^2-263*n+180)*a(n-2) +4*(-2*n^2-10*n+57)*a(n-3) +60*(n-4)^2*a(n-4) -6*(2*n-7)*(n-5)*a(n-5)=0. - R. J. Mathar, Dec 03 2014

Conjecture: 3*n*(n-1)*(57*n-136)*a(n) +(n-1)*(171*n^2-415*n+14)*a(n-1) +2*(532*n^3-2281*n^2+2755*n-840)*a(n-2) -2*(n-3)*(304*n^2-835*n+216)*a(n-3) +2*(19*n-5)*(n-4)*(2*n-5)*a(n-4)=0. - R. J. Mathar, Dec 03 2014

Crossrefs

Sequence in context: A332616 A097348 A271034 * A106193 A334875 A328476

Adjacent sequences: A185962 A185963 A185964 * A185966 A185967 A185968

Keyword

sign,easy

Author

Paul Barry, Feb 07 2011

Status

approved