A364792 G.f. satisfies A(x) = 1 + x*A(x)^4 / (1 - x*A(x)^2).

1, 1, 5, 33, 250, 2054, 17800, 160183, 1482535, 14022415, 134943095, 1317046306, 13005842030, 129708875695, 1304588594925, 13217663310305, 134775670244250, 1382019265706377, 14242560597119165, 147435736533094415, 1532365596794307010

Offset

0,3

Links

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

Formula

a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(4*n-2*k,n-1-k) for n > 0.

D-finite with recurrence 3*n*(36653*n-48128)*(3*n-1)*(3*n+1)*a(n) +5*(-2160545*n^4 +5139476*n^3 -2463019*n^2 -1385144*n +913296)*a(n-1) +4*(-948403*n^4 +17991137*n^3 -77629283*n^2 +126107767*n -70578450)*a(n-2) +10*(n-3)*(599072*n^3 -5090881*n^2 +13501042*n -11263100)*a(n-3) -50*(6861*n-12886)*(n-3) *(n-4)*(2*n-7)*a(n-4)=0. - R. J. Mathar, Aug 10 2023

Maple

A364792 := proc(n)
    if n = 0 then
        1;
    else
        add( binomial(n, k) * binomial(4*n-2*k, n-1-k), k=0..n-1) ;
        %/n ;
    end if ;
end proc:
seq(A364792(n), n=0..80); # R. J. Mathar, Aug 10 2023

Prog

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

Crossrefs

Cf. A002293, A243659, A349331, A364747, A364765.

Sequence in context: A034015 A268563 A056159 * A367280 A171804 A365182

Adjacent sequences: A364789 A364790 A364791 * A364793 A364794 A364795

Keyword

nonn

Author

Seiichi Manyama, Aug 08 2023

Status

approved