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 A091346 Binomial convolution of A069321(n), where A069321(0)=0, with the sequence of all ones alternating in sign. 3
 0, 1, 3, 19, 135, 1171, 11823, 136459, 1771815, 25561891, 405658143, 7022891899, 131714587095, 2660335742611, 57570797744463, 1328913670495339, 32592691757283975, 846383665814211331, 23200396829832102783 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n)=Sum(C(n, k)(-1)^(n-k)Sum(i!i Stirling2(k, i), i=1, .., k), k=0, .., n). E.g.f.: ((exp(x)-1)/(2-exp(x))^2)*exp(-x). a(n) = (A000670(n+1)+(-1)^(n+1))/4. - Vladeta Jovovic, Jan 17 2005 G.f.: x/(1+x)/Q(0), where Q(k) = 1 - x*(3*k+4) - 2*x^2*(k+1)*(k+3)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 03 2013 a(n) ~ n! * n / (8 * (log(2))^(n+2)). - Vaclav Kotesovec, Nov 27 2017 MATHEMATICA Table[Sum[Binomial[n, k](-1)^(n-k)Sum[i!i StirlingS2[k, i], {i, 1, k}], {k, 0, n}], {n, 0, 20}] CROSSREFS Cf. A083410. Sequence in context: A226459 A256092 A074567 * A035086 A215852 A105797 Adjacent sequences:  A091343 A091344 A091345 * A091347 A091348 A091349 KEYWORD easy,nonn AUTHOR Mario Catalani (mario.catalani(AT)unito.it), Jan 02 2004 STATUS approved

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Last modified March 18 01:15 EDT 2018. Contains 300613 sequences. (Running on oeis4.)