A066224 Bisection of A000085.
1, 4, 26, 232, 2620, 35696, 568504, 10349536, 211799312, 4809701440, 119952692896, 3257843882624, 95680443760576, 3020676745975552, 101990226254706560, 3666624057550245376, 139813029266338603264
Offset: 0
Programs
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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
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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