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 A059371 a(n) = (n-1)! + ((n+1)/2)*a(n-1), a(1)=0. 7
 1, 4, 16, 72, 372, 2208, 14976, 115200, 996480, 9607680, 102366720, 1195568640, 15193785600, 208728576000, 3081867264000, 48659595264000, 817953583104000, 14581909536768000, 274755150544896000, 5455208664170496000, 113825841809670144000 (list; graph; refs; listen; history; text; internal format)
 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 *) 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: A152807 A217461 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

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Last modified January 19 03:18 EST 2019. Contains 319282 sequences. (Running on oeis4.)