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

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..757

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

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

Prog

(PARI) a(n) = (-1)^n*sum(k=0, n, (-3)^k*binomial(n, k)*binomial(3*n+k+1, n)/(3*n+k+1));

Crossrefs

Cf. A025192, A107841, A235347, A364826, A364827.

Cf. A144097, A243659.

Sequence in context: A355723 A227934 A349652 * A245112 A260332 A254999

Adjacent sequences: A364822 A364823 A364824 * A364826 A364827 A364828

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2023

Status

approved