A107026 - OEIS

%I #5 Feb 20 2015 17:34:10

%S 1,2,10,62,426,3112,23686,185684,1488554,12144248,100489320,841268078,

%T 7112138790,60629940152,520591221412,4498091003272,39079909924522,

%U 341193986978008,2991881019936760,26338436818801496,232688056611178216

%N Row sums of inverse of Riordan array (1/(1+x),x/(1+x)^4).

%C The Riordan array (1/(1+x),x/(1+x)^4) has general term (-1)^(n-k)*binomial(n+3k,4k).

%F G.f.: A(x)=y satisfies (2y)^4*x-(y+1)^3*(y-1)=0; a(n)=3*binomial(4n, n)-2*sum{k=0..n, binomial(4n, k)}.

%F Conjecture: +189*n*(3*n-1)*(3*n-2)*a(n) +72*(-1034*n^3+3098*n^2-3754*n+1655)*a(n

%F -1) +384*(2700*n^3-12828*n^2+20426*n-10785)*a(n-2) +4096*(-1066*n^3+6666*n^2-129

%F 50*n+7365)*a(n-3) -65536*(4*n-15)*(2*n-7)*(4*n-13)*a(n-4)=0. - _R. J. Mathar_, Feb 20 2015

%F Conjecture: 3*n*(3*n-1)*(3*n-2)*(22*n^2-62*n+43)*a(n) +8*(-1892*n^5+8280*n^4-13330*n^3+9660*n^2-3048*n+315)*a(n-1) +128*(4*n-7)*(2*n-3)*(4*n-5)*(22*n^2-18*n+3)*a(n-2)=0. - _R. J. Mathar_, Feb 20 2015

%p A107026 := proc(n)

%p     3*binomial(4*n,n)-2*add(binomial(4*n,k),k=0..n) ;

%p end proc: # _R. J. Mathar_, Feb 20 2015

%Y Cf. A047098.

%K easy,nonn

%O 0,2

%A _Paul Barry_, May 09 2005