A392619 a(n) = denominator((2^n*(n!)^2/(1+2*n)!)^2).

1, 9, 225, 1225, 99225, 480249, 9018009, 41409225, 11967266025, 53335593025, 940839860961, 4113258565689, 285642955950625, 1232152159100625, 21147754404155625, 90324408810638025, 98363281194784809225, 416937783611112080625, 7046763281032252325625, 29690102355817329050625

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = denominator((n!/Product_{i=1..n} 1 + 2*i)^2).

A124399(n)/a(n) ~ Pi/(4^(n+1)*n).

a(2*n+1)/a(2*n) ~ 4.

Mathematica

a[n_]:=Denominator[(2^n*n!^2/(1+2n)!)^2]; Array[a, 20, 0]

Crossrefs

Cf. A124399 (numerators).

Cf. A000079, A000142, A001044, A002697, A009445, A134374.

Sequence in context: A167038 A074190 A069075 * A218659 A012054 A067405

Adjacent sequences: A392616 A392617 A392618 * A392620 A392621 A392622

Keyword

nonn,frac

Author

Stefano Spezia, Jan 17 2026

Status

approved