A364825 G.f. satisfies A(x) = 1 - x*A(x)^3 * (1 - 3*A(x)).
1, 2, 18, 222, 3166, 49098, 804138, 13686198, 239671590, 4290463698, 78160665666, 1444298971662, 27005948771886, 510024567278234, 9714561608833242, 186403770207998310, 3599812021110287862, 69914211761486437026, 1364692279095996581490
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..757
Programs
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Maple
A364825 := proc(n) (-1)^n*add( (-3)^k*binomial(n,k) * binomial(3*n+k+1,n)/(3*n+k+1),k=0..n) ; end proc: seq(A364825(n),n=0..80); # R. J. Mathar, Aug 10 2023
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PARI
a(n) = (-1)^n*sum(k=0, n, (-3)^k*binomial(n, k)*binomial(3*n+k+1, n)/(3*n+k+1));
Formula
a(n) = (-1)^n * Sum_{k=0..n} (-3)^k * binomial(n,k) * binomial(3*n+k+1,n) / (3*n+k+1).
a(n) = (1/n) * Sum_{k=0..n-1} 2^(n-k) * binomial(n,k) * binomial(4*n-k,n-1-k) for n > 0.
a(n) = (1/n) * Sum_{k=1..n} 2^k * 3^(n-k) * binomial(n,k) * binomial(3*n,k-1) for n > 0.
D-finite with recurrence +2079*n*(3*n-1)*(3*n+1)*a(n) +(-347173*n^3 +395007*n^2 -41030*n -43092)*a(n-1) +18*(-59207*n^3 +325826*n^2 -590255*n +352406)*a(n-2) +3*(-3299*n^3 +35998*n^2 -125399*n +141144)*a(n-3) +9*(3*n-10)*(3*n-11) *(n-4)*a(n-4)=0. - R. J. Mathar, Aug 10 2023