A384253 - OEIS

A384253

a(n) = 1 + ((1+(-1)^(n-1))*(n-1)!)/(n+1).

2, 1, 2, 1, 9, 1, 181, 1, 8065, 1, 604801, 1, 68428801, 1, 10897286401, 1, 2324754432001, 1, 640237370572801, 1, 221172909834240001, 1, 93666727314800640001, 1, 47726800133326110720001, 1, 28806532937614688256000001, 1, 20325889640780924033433600001, 1, 16578303738261941164769280000001

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..31.

Ivan V. Morozov, On Quotients of a More General Theorem of Wilson, arXiv:2505.16201 [math.NT], 2025. See Z formula (7) p. 2 and p. 9.

FORMULA

a(2*n+1) = 1 + A060593(n), a(2n) = 1.

D-finite with recurrence (n+1)*a(n) -(n-2)*(n-1)^2*a(n-2) +(n-3)*(n^2-n+1)=0. - R. J. Mathar, May 26 2025

PROG

(PARI) a(n) = 1 + ((1+(-1)^(n-1))*(n-1)!)/(n+1);

CROSSREFS