A376486 G.f. satisfies A(x) = 1 / (1 - x^3*A(x)^3 * (1 + x)).

1, 0, 0, 1, 1, 0, 4, 8, 4, 22, 66, 66, 162, 560, 840, 1529, 4985, 9690, 16774, 47349, 107229, 195500, 483000, 1172724, 2311516, 5249556, 12910716, 27299992, 59765400, 144602352, 321554224, 700449496, 1654540452, 3789265198, 8344514618, 19327204006

Offset: 0

Author

Seiichi Manyama, Sep 25 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A005043, A052709, A376487.

Programs

Maple

A376486 := proc(n)
    add(binomial(4*k,k)*binomial(k,n-3*k)/(3*k+1),k=0..floor(n/3)) ;
end proc:
seq(A376486(n),n=0..70) ;
# R. J. Mathar, Sep 26 2024

PARI

a(n) = sum(k=0, n\3, binomial(4*k, k)*binomial(k, n-3*k)/(3*k+1));

Formula

G.f.: (1/x) * Series_Reversion( x*(1-x^3)/(1+x^4) ).

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

D-finite with recurrence 243*n*(n-1)*(n+1)*a(n) +81*n*(n-1)*(14*n-31)*a(n-1) +27*(73*n-240)*(n-1)*(n-2)*a(n-2) +36*(-22*n^3-99*n^2+731*n-870)*a(n-3) +48*(-263*n^3+1908*n^2-4449*n+3290)*a(n-4) -128*(n-4)*(230*n^2-1429*n+2205)*a(n-5) -768*(n-5)*(43*n-168)*(n-4)*a(n-6) -9216*(n-5)*(n-6)*(2*n-9)*a(n-7) -4096*(n-5)*(n-6)*(n-7)*a(n-8)=0. - R. J. Mathar, Sep 26 2024