A364374 G.f. satisfies A(x) = (1 + x*A(x)) * (1 - x*A(x)^2).

1, 0, -1, 1, 2, -6, -1, 28, -31, -98, 288, 131, -1730, 1638, 7431, -19583, -15502, 135642, -99523, -664050, 1535896, 1816196, -11902728, 5944326, 64487669, -129346490, -213116764, 1112382523, -277762230, -6572175490, 11287106695, 25078981772, -107983368519, -1826241850

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

D-finite with recurrence 15*n*(n+1)*a(n) +2*n*(13*n-11)*a(n-1) +12*(9*n^2-19*n+9)*a(n-2) +2*(10*n^2-65*n+99)*a(n-3) -4*(n-3)*(2*n-7)*a(n-4)=0. - R. J. Mathar, Jul 25 2023

A(x) = (1/x) * series_reversion(x*(1 + x + x^2)/(1 + x)). - Peter Bala, Sep 08 2024

Maple

A364374 := proc(n)
    add( (-1)^k*binomial(n+k+1, k) * binomial(n+k+1, n-k)/(n+k+1), k=0..n) ;
end proc:
seq(A364374(n), n=0..80); # R. J. Mathar, Jul 25 2023

Mathematica

nmax = 33;
A[_] = 1;
Do[A[x_] = (1+x*A[x])*(1-x*A[x]^2) + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 21 2023 *)

Prog

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

Crossrefs

Cf. A364375, A364376.

Cf. A057078, A007863, A364371.

Sequence in context: A281635 A180512 A132181 * A291646 A366152 A366427

Adjacent sequences: A364371 A364372 A364373 * A364375 A364376 A364377

Keyword

sign,easy

Author

Seiichi Manyama, Jul 21 2023

Status

approved