cp's OEIS Frontend

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

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

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

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

Conjecture D-finite with recurrence +3*n*(16543753*n -26995933)*(3*n-1)*(3*n-2)*a(n) +(-1669899251*n^4 -26931977989*n^3 +131963667975*n^2 -188283072995*n +85757456660)*a(n-1) +2*(-61301926003*n^4 +515926265010*n^3 -1655392333929*n^2 +2311146075302*n -1165379619540)*a(n-2) -96*(39221117*n -50949760)*(4*n-9)*(2*n-5)*(4*n-7)*a(n-3)=0. - R. J. Mathar, Aug 19 2025

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

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

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

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

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

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

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

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

D-finite with recurrence n*(n+1)*a(n) +42*n*(n-2)*a(n-1) +12*(-33*n^2+120*n-95)*a(n-2) +72*(-63*n^2+189*n-110)*a(n-3) +3456*(3*n-8)*(3*n-10)*a(n-4)=0. - R. J. Mathar, Aug 19 2025