A066224 Bisection of A000085.

1, 4, 26, 232, 2620, 35696, 568504, 10349536, 211799312, 4809701440, 119952692896, 3257843882624, 95680443760576, 3020676745975552, 101990226254706560, 3666624057550245376, 139813029266338603264

Offset: 0

Author

N. J. A. Sloane, Dec 19 2001

Keywords

• nonn
• easy

Crossrefs

Cf. A066223.

Unsigned row sums of A130757.

Programs

Maple

a := proc(n) option remember: if n = 0 then RETURN(1) fi: if n = 1 then RETURN(1) fi: a(n-1)+(n-1)*a(n-2): end: for i from 1 to 61 by 2 do printf(`%d,`,a(i)) od: # James Sellers, Feb 11 2002

Mathematica

Table[n! 2^n LaguerreL[n,1/2,-1/2],{n,0,20}] (* Harvey P. Dale, Mar 11 2013 *)
Table[(-2)^n HypergeometricU[-n, 3/2, -(1/2)], {n, 0, 90}] (* Emanuele Munarini, Aug 31 2017 *)

Formula

a(n) = n!*2^n*LaguerreL(n, 1/2, -1/2). - Vladeta Jovovic, May 10 2003

a(n) = sum(n!*(2^(n-m))*binomial(n+1/2,n-m)/m!,m=0..n), n>=0.

a(n) ~ n^(n+1/2)*2^n*exp(-n+sqrt(2*n)-1/4) * (1 + 19/(24*sqrt(2*n))). - Vaclav Kotesovec, Jun 22 2013

a(n+2) - 4*(n+2)*a(n+1) + 2*(n+1)*(2*n+3)*a(n) = 0 - Emanuele Munarini, Aug 31 2017

Extensions

More terms from James Sellers, Feb 11 2002