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Bisection of A000085.
2

%I #26 Aug 31 2017 11:15:42

%S 1,4,26,232,2620,35696,568504,10349536,211799312,4809701440,

%T 119952692896,3257843882624,95680443760576,3020676745975552,

%U 101990226254706560,3666624057550245376,139813029266338603264

%N Bisection of A000085.

%F a(n) = n!*2^n*LaguerreL(n, 1/2, -1/2). - _Vladeta Jovovic_, May 10 2003

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

%F 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

%F a(n+2) - 4*(n+2)*a(n+1) + 2*(n+1)*(2*n+3)*a(n) = 0 - _Emanuele Munarini_, Aug 31 2017

%p 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 A. Sellers_, Feb 11 2002

%t Table[n! 2^n LaguerreL[n,1/2,-1/2],{n,0,20}] (* _Harvey P. Dale_, Mar 11 2013 *)

%t Table[(-2)^n HypergeometricU[-n, 3/2, -(1/2)], {n, 0, 90}] (* _Emanuele Munarini_, Aug 31 2017 *)

%Y Cf. A066223.

%Y Unsigned row sums of A130757.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 19 2001

%E More terms from _James A. Sellers_, Feb 11 2002