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 A194004 E.g.f.: A(x) = -log(3-exp(x)-exp(x^2)). 0
 0, 1, 4, 12, 86, 590, 6032, 66948, 913754, 13855542, 239928992, 4579666916, 96564964322, 2216227508118, 55168605200984, 1478010072581076, 42439794637684826, 1299629513716412246, 42289878531064635632, 1456983891928235324292, 52986585444052122288146 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..20. FORMULA a(n) = n!*sum(k=1..n, (k-1)!*sum(j=0..k, sum(m=floor((k-j)/2)..(n-j)/2, (stirling2(n-2*m,j)*stirling2(m,k-j))/((n-2*m)!*(m!))))). a(n) ~ (n-1)!/r^n, where r = 0.522452131474223... is the root of the equation exp(r)+exp(r^2) = 3. - Vaclav Kotesovec, Jun 27 2013 MATHEMATICA CoefficientList[Series[-Log[3-E^x-E^(x^2)], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *) PROG (Maxima) a(n):=n!*sum((k-1)!*sum(sum((stirling2(n-2*m, j)*stirling2(m, k-j))/((n-2*m)!*(m!)), m, floor((k-j)/2), (n-j)/2), j, 0, k), k, 1, n); CROSSREFS Sequence in context: A226960 A081214 A331087 * A064280 A203379 A209031 Adjacent sequences: A194001 A194002 A194003 * A194005 A194006 A194007 KEYWORD nonn AUTHOR Vladimir Kruchinin, Aug 10 2011 STATUS approved

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Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)