cp's OEIS Frontend

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

a(n) = [x^n] ( (1+2*x)^2/(1-3*x) )^n.

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-3*x) / (1+2*x)^2 ). See A386772.

a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(2*n,k).

D-finite with recurrence 9*n*a(n) +6*(-18*n-5)*a(n-1) +80*(-17*n+37)*a(n-2) +800*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Aug 03 2025

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

a(n) = [x^n] ( (1+2*x)^3/(1-3*x)^2 )^n.

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-3*x)^2 / (1+2*x)^3 ). See A386773.

a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(3*n,k).

D-finite with recurrence 54*n*(2*n-1)*a(n) +3*(-2063*n^2+4087*n-2340)*a(n-1) +4*(21379*n^2-81239*n+73110)*a(n-2) +50*(277*n^2-6323*n+15702)*a(n-3) -8400*(3*n-10)*(3*n-11)*a(n-4)=0. - R. J. Mathar, Aug 03 2025

a(n) = [x^n] (1+2*x)^(4*n+1)/(1-3*x)^(3*n+1).

a(n) = [x^n] 1/((1-2*x) * (1-5*x)^(3*n+1)).

a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(4*n+1,k).

a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * binomial(3*n+k,k).

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

a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^4 / (1-3*x)^3 )^(n+1).