OFFSET
1,3
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..200
FORMULA
Recurrence: 2*(n-3)*(9*n-64)*a(n) = 2*(18*n^3 - 182*n^2 + 423*n - 149)*a(n-1) - 2*(n-1)*(9*n^3 - 91*n^2 + 243*n - 173)*a(n-2) + 6*(n-2)*(n-1)*(n+1)*a(n-3) + (n-3)*(n-2)*(n-1)*(9*n^2 - 91*n + 224)*a(n-4) - (n-4)*(n-3)*(n-2)*(n-1)*(9*n-67)*a(n-5) + (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n-55)*a(n-6). - Vaclav Kotesovec, Feb 09 2014
a(n) ~ exp(sqrt(2*n)-n-1/2) * n^n / sqrt(2) * (1 + 19/(24*sqrt(2*n))). - Vaclav Kotesovec, Feb 09 2014
E.g.f.: exp(1/(1-x)/2 - 1/2 + log(1/(1-x))/2-x^2/4) - exp(x+x^2/2!). - Joerg Arndt, Jul 24 2016
MATHEMATICA
nn = 20; Drop[Range[0, nn]! CoefficientList[Series[Exp[1/(1 - z)/2 - 1/2 + Log[1/(1 - z)]/2 - z^2/4] - Exp[z + z^2/2!], {z, 0, nn}], z], 1] (* Geoffrey Critzer, Jul 23 2016 *)
PROG
(PARI) x='x+O('x^22); concat( [0, 0], Vec( serlaplace( exp(1/(1-x)/2 - 1/2 + log(1/(1-x))/2-x^2/4) - exp(x+x^2/2!) ) ) ) \\ Joerg Arndt, Jul 24 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Don Knuth, Mar 31 2008
EXTENSIONS
More terms from Alois P. Heinz, Sep 12 2008
STATUS
approved