cp's OEIS Frontend

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(n-1,n-k).

D-finite with recurrence 96*(3*n+2)*(3*n+1)*(n+1)*a(n) +4*(-4121*n^3 +1922*n^2 -1273*n+124)*a(n-1) +4*(20588*n^3 -76648*n^2 +98677*n -43586)*a(n-2) +(-90073*n^3 +671565*n^2 -1665278*n +1375320)*a(n-3) +210*(n-4)*(3*n-7) *(3*n-8)*a(n-4)=0. - R. J. Mathar, Jan 25 2024

From Seiichi Manyama, Dec 02 2024: (Start)

G.f.: exp( Sum_{k>=1} A378612(k) * x^k/k ).

a(n) = (1/(n+1)) * [x^n] 1/(1 - x/(1 - x))^(3*(n+1)).

G.f.: B(x)^3 where B(x) is the g.f. of A243659.

a(n) = 3 * Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(n,k) * binomial(3*n+k+3,n)/(3*n+k+3). (End)

a(n) = [x^n] 1/(1 - x/(1 - x))^(4*n).

a(n) = (1/8)^n * [x^(4*n)] 4/(1 - x/(1 - x))^n for n > 0.

G.f.: exp( 1/2 * Sum_{k>=1} A378613(k) * x^k/k ).

G.f.: B(x)^2 where B(x) is the g.f. of A243667.

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

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

G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/2)/(1 - x*A(x)^2) )^2.

G.f.: exp( 3/4 * Sum_{k>=1} A378613(k) * x^k/k ).

G.f.: B(x)^3 where B(x) is the g.f. of A243667.

a(n) = 3 * Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(n,k) * binomial(4*n+k+3,n)/(4*n+k+3).

a(n) = 3 * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(n-1,n-k)/(4*n+k+3).

G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/3)/(1 - x*A(x)^(4/3)) )^3.