A364430 G.f. satisfies A(x) = 1 - x*A(x)*(1 - 2*A(x)^3).

1, 1, 7, 61, 603, 6443, 72517, 846995, 10170685, 124780525, 1557347467, 19710577873, 252386341335, 3263626001751, 42558647522697, 559032393114023, 7390085367865081, 98242108076244665, 1312529311579827631, 17613845480108029957, 237322279651518516019

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) +(-566*n^3 +1335*n^2 -1105*n +312)*a(n-1) +3*(943*n^3 -5739*n^2 +11016*n -6748)*a(n-2) +18*(-250*n^3 +2499*n^2 -8233*n +8938)*a(n-3) +27*(n-4)*(31*n^2 -314*n +735)*a(n-4) +81*(10*n -51)*(n-4) *(n-5)*a(n-5) +243*(n-5) *(n-6)*(n-4)*a(n-6)=0. - R. J. Mathar, Jul 25 2023

Maple

A364430 := proc(n)
    (-1)^n*add((-2)^k* binomial(n, k) * binomial(n+3*k+1, n) / (n+3*k+1), k=0..n) ;
end proc:
seq(A364430(n), n=0..70); # R. J. Mathar, Jul 25 2023

Prog

(PARI) a(n) = (-1)^n*sum(k=0, n, (-2)^k*binomial(n, k)*binomial(n+3*k+1, n)/(n+3*k+1));

Crossrefs

Cf. A001003, A153232.

Cf. A364431, A364432, A364437.

Sequence in context: A199686 A113718 A177132 * A077642 A071172 A259335

Adjacent sequences: A364427 A364428 A364429 * A364431 A364432 A364433

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2023

Status

approved