A371341 G.f. A(x) satisfies A(x) = 1 + x/A(x) * (1 + A(x)^5).

1, 2, 6, 46, 330, 2778, 24094, 219318, 2048274, 19583410, 190497142, 1880184446, 18778814938, 189456108554, 1927852050830, 19763367194630, 203919590002210, 2116079501498722, 22069907395614182, 231222485352688590, 2432325883912444010

Offset: 0

Author

Seiichi Manyama, Apr 12 2024

Keywords

• nonn

Crossrefs

Cf. A112478, A348957, A364394, A364395, A366363, A371892.

Programs

Maple

A371341 := proc(n)
    if n = 0 then
        1;
    else
        add(binomial(n,k)*binomial(2*n-5*k-2,n-1),k=0..n) ;
        (-1)^(n-1)*%/n ;
    end if;
end proc:
seq(A371341(n),n=0..60) ; # R. J. Mathar, Apr 22 2024

PARI

a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(2*n-5*k-2, n-1))/n);

Formula

a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(2*n-5*k-2,n-1) for n > 0.