A381779 - OEIS

%I #7 Mar 07 2025 10:47:40

%S 1,2,11,95,977,11028,132029,1646428,21155077,278127359,3723466202,

%T 50586670945,695676081162,9665426437561,135464096419620,

%U 1912922793362142,27190770354633287,388734441118885467,5586079818959767743,80638973170989453862,1168864771263296930809

%N G.f. A(x) satisfies A(x) = (1 + x*A(x)) * C(x*A(x)^3), where C(x) is the g.f. of A000108.

%F a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(n+2*k+1,n-k)/(n+4*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(n+2*k+1, n-k)/(n+4*k+1));

%Y Cf. A054727, A381778.

%Y Cf. A000108.

%K nonn,new

%O 0,2

%A _Seiichi Manyama_, Mar 07 2025