A059371 a(n) = (n-1)! + ((n+1)/2)*a(n-1), a(1)=0.

1, 4, 16, 72, 372, 2208, 14976, 115200, 996480, 9607680, 102366720, 1195568640, 15193785600, 208728576000, 3081867264000, 48659595264000, 817953583104000, 14581909536768000, 274755150544896000, 5455208664170496000, 113825841809670144000

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

Second diagonal of triangle in A059369.

Sequence in context: A217461 A370276 A129872 * A208528 A007234 A096244

Adjacent sequences: A059368 A059369 A059370 * A059372 A059373 A059374

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