OFFSET
2,2
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 171, #34.
LINKS
Harry J. Smith, Table of n, a(n) for n = 2..200
FORMULA
E.g.f.: (x^2-2*x-2*log(1-x))/(x-2)^2. - Vladeta Jovovic, May 04 2003
a(n) = Sum_{i=1..n-1} i!*(n-i)!. E.g., a(6) = 1!*5!+2!4!+3!3!+4!2!+5!1! = 120+48+36+48+120 = 372. - Jon Perry, May 06 2006
a(n) = 2*Integral_{t>=0}t^n*exp(-t)*(t*exp(-t)*Ei(t)-1), with Ei the exponential integral function.
Recurrence: 2*a(n) = (3*n-1)*a(n-1) - (n-1)*n*a(n-2). - Vaclav Kotesovec, Aug 11 2013
a(n) ~ 2*(n-1)!. - Vaclav Kotesovec, Aug 11 2013
a(n) = -2*n! - 2*(n+1)!*Re(LerchPhi(2, 1, 2 + n)). - Vladimir Reshetnikov, Oct 17 2015
a(n) = n!*Re(hypergeom([1,1],[n+2],2) - 1). - Vladimir Reshetnikov, Oct 19 2015
MAPLE
series(hypergeom([1, 2], [], x)^2, x=0, 30); # Mark van Hoeij, Apr 20 2013
MATHEMATICA
Rest[Rest[CoefficientList[Series[(x^2-2*x-2*Log[1-x])/(x-2)^2, {x, 0, 20}], x]* Range[0, 20]!]] (* Vaclav Kotesovec, Aug 11 2013 *)
Table[-2 n! - 2 (n + 1)! Re[LerchPhi[2, 1, 2 + n]], {n, 2, 10}] (* Vladimir Reshetnikov, Oct 17 2015 *)
Table[2*Sum[(2^k - 1) * Abs[StirlingS1[n, k]] * BernoulliB[k], {k, 0, n}], {n, 3,
25}] (* Vaclav Kotesovec, Oct 04 2022 *)
PROG
(PARI) a(n)=sum(i=1, n-1, i!*(n-i)!) \\ Jon Perry, May 06 2006
(PARI) { a=0; for (n = 2, 200, write("b059371.txt", n, " ", a = (n - 1)! + a*(n + 1)/2); ) } \\ Harry J. Smith, Jun 26 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 28 2001
EXTENSIONS
Better description from Vladeta Jovovic, May 04 2003
More terms from Larry Reeves (larryr(AT)acm.org), Jan 31 2001
STATUS
approved