A364330 G.f. satisfies A(x) = (1 + x^4) * (1 + x*A(x)^2).

1, 1, 2, 5, 15, 45, 142, 464, 1556, 5327, 18532, 65326, 232826, 837589, 3037472, 11092143, 40753626, 150541422, 558762382, 2082871613, 7794301294, 29269317708, 110263451242, 416595676681, 1578183767068, 5993326380378, 22812048907856, 87010994947971, 332531385362972

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

G.f.: A(x) = 2*(1 + x^4) / (1 + sqrt(1-4*x*(1 + x^4)^2)).

a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-8*k+1,k) * binomial(2*n-8*k+1,n-4*k) / (2*n-8*k+1).

D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(n+1)*a(n-4) +6*(-2*n+9)*a(n-5) +6*(-2*n+17)*a(n-9) +2*(-2*n+25)*a(n-13)=0. - R. J. Mathar, Jul 25 2023

Maple

A364330 := proc(n)
    add( binomial(2*n-8*k+1, k) * binomial(2*n-8*k+1, n-4*k)/(2*n-8*k+1), k=0..n/4) ;
end proc:
seq(A364330(n), n=0..80); # R. J. Mathar, Jul 25 2023

Mathematica

nmax = 28; A[_] = 1;
Do[A[x_] = (1 + x^4)*(1 + x*A[x]^2) + O[x]^(nmax+1) // Normal, {nmax+1}];
CoefficientList[A[x], x] (* Jean-François Alcover, Mar 03 2024 *)

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(2*n-8*k+1, k)*binomial(2*n-8*k+1, n-4*k)/(2*n-8*k+1));

Crossrefs

Cf. A073157, A215576, A364329.

Sequence in context: A254534 A071727 A148354 * A151279 A149907 A148355

Adjacent sequences: A364327 A364328 A364329 * A364331 A364332 A364333

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 18 2023

Status

approved