%I #11 Dec 09 2024 15:43:47
%S 1,7,97,1519,25089,427007,7408897,130287871,2313945089,41409732607,
%T 745530884097,13488086405119,245014271688705,4465915098890239,
%U 81637668328243201,1496095489290731519,27477504726883368961,505627095685486608383,9320167322334416338945
%N a(n) = Sum_{k=0..n} binomial(4*n,k) * binomial(4*n-k-1,n-k).
%F a(n) = [x^n] ( (1+x)^4/(1-x)^3 )^n.
%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x*(1-x)^3/(1+x)^4 ). See A365846.
%t Table[Sum[Binomial[4n,k]Binomial[4n-k-1,n-k],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Dec 09 2024 *)
%o (PARI) a(n) = sum(k=0, n, binomial(4*n, k)*binomial(4*n-k-1, n-k));
%Y Cf. A001448, A370100, A370102.
%Y Cf. A365846.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 10 2024