A364394 G.f. satisfies A(x) = 1 + x/A(x)*(1 + 1/A(x)).

1, 2, -6, 34, -238, 1858, -15510, 135490, -1223134, 11320066, -106830502, 1024144482, -9945711566, 97634828354, -967298498358, 9659274283650, -97119829841854, 982391779220482, -9990160542904134, 102074758837531810, -1047391288012377774, 10788532748880319298

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A027307.

a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(2*n+k-2,n-1) = (-1)^(n-1) * A108424(n) for n > 0.

D-finite with recurrence n*(2*n-1)*a(n) +3*(6*n^2-10*n+3)*a(n-1) +(-46*n^2+227*n-279)*a(n-2) +2*(n-3)*(2*n-7)*a(n-3)=0. - R. J. Mathar, Jul 25 2023

a(n) ~ c*(-1)^(n-1)*4^n*2F1([-n, 2*n-1], [n], -1)*n^(-3/2), with c = 1/(4*sqrt(Pi)) = A087197/4. - Stefano Spezia, Oct 21 2023

Maple

A364394 := proc(n)
    if n = 0 then
        1;
    else
    (-1)^(n-1)*add( binomial(n, k) * binomial(2*n+k-2, n-1), k=0..n)/n ;
    end if;
end proc:
seq(A364394(n), n=0..80); # R. J. Mathar, Jul 25 2023

Prog

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

Crossrefs

Cf. A112478, A364396, A364398.

Cf. A027307, A087197, A108424.

Sequence in context: A019029 A019032 A108424 * A328884 A002685 A262391

Adjacent sequences: A364391 A364392 A364393 * A364395 A364396 A364397

Keyword

sign

Author

Seiichi Manyama, Jul 22 2023

Status

approved