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A107026 Row sums of inverse of Riordan array (1/(1+x),x/(1+x)^4).

%I A107026 #11 Mar 16 2025 09:39:29
%S A107026 1,2,10,62,426,3112,23686,185684,1488554,12144248,100489320,841268078,
%T A107026 7112138790,60629940152,520591221412,4498091003272,39079909924522,
%U A107026 341193986978008,2991881019936760,26338436818801496,232688056611178216
%N A107026 Row sums of inverse of Riordan array (1/(1+x),x/(1+x)^4).
%C A107026 The Riordan array (1/(1+x),x/(1+x)^4) has general term (-1)^(n-k)*binomial(n+3k,4k).
%F A107026 G.f.: A(x)=y satisfies (2y)^4*x-(y+1)^3*(y-1)=0.
%F A107026 a(n) = 3*binomial(4*n, n) - 2*Sum_{k=0..n} binomial(4*n, k).
%F A107026 Conjecture: +189*n*(3*n-1)*(3*n-2)*a(n) +72*(-1034*n^3+3098*n^2-3754*n+1655)*a(n
%F A107026 -1) +384*(2700*n^3-12828*n^2+20426*n-10785)*a(n-2) +4096*(-1066*n^3+6666*n^2-129
%F A107026 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 A107026 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 A107026 := proc(n)
%p A107026     3*binomial(4*n,n)-2*add(binomial(4*n,k),k=0..n) ;
%p A107026 end proc: # _R. J. Mathar_, Feb 20 2015
%Y A107026 Cf. A047098, A107027, A107030.
%K A107026 easy,nonn
%O A107026 0,2
%A A107026 _Paul Barry_, May 09 2005