A101269 a(1)=0, a(2)=1, a(n+2) = (8*n^2+2*n+1)*a(n+1) - 2*n*(2*n-1)^3*a(n).

0, 1, 11, 299, 15371, 1285371, 159158691, 27376820379, 6246962876475, 1826295061189275, 665694890795056275, 296004348848796457275, 157710301268790933578475, 99189386694727572925906875

Offset

1,3

Links

Table of n, a(n) for n=1..14.

Ofer Yifrach-Stav, Fast and Private Pool Testing and Contributions to Experimental Mathematics, Doctoral thesis, École normale supérieure (Paris, France), HAL Science [math.cs] 2024, Art. No. tel-04513104. See p. 222.

Formula

a(n+1) = (2*n)!*(2*G*binomial(2*n, n)/4^n - Integral_{t=0..oo} t/cosh(t)^(2*n+1) dt) where G = 0.915965594... is Catalan's constant.

a(n) = (2*n-4)! + (2*n-3)^2*a(n-1) for n = 2, 3, ... with a(1) = 0. - Johannes W. Meijer, May 24 2009

Mathematica

RecurrenceTable[{a[1]==0, a[2]==1, a[n]==(8(n-2)^2+2(n-2)+1)a[n-1]- 2(n-2)(2(n-2)-1)^3 a[n-2]}, a, {n, 20}] (* Harvey P. Dale, May 06 2013 *)

Prog

(PARI) a(n)=if(n<3, (n+1)%2, (8*(n-2)^2+2*(n-2)+1)*a(n-1)-2*(n-2)*(2*(n-2)-1)^3*a(n-2)) \\ Benoit Cloitre, Dec 02 2005

Crossrefs

Cf. A006752.

For n >= 1, equals the first left hand column of the Beta triangle A160480. The second left hand column is A160482. - Johannes W. Meijer, May 24 2009

Sequence in context: A213256 A067424 A001538 * A012184 A012027 A279181

Adjacent sequences: A101266 A101267 A101268 * A101270 A101271 A101272

Keyword

nonn

Author

Benoit Cloitre, Dec 18 2004

Status

approved