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 A193931 E.g.f. A(x)=exp(x+x^2+x^3+x^4+x^5) 0
 1, 1, 3, 13, 73, 501, 3331, 27553, 253233, 2540233, 27340291, 309811701, 3843476473, 50560182973, 701098196163, 10205952248521, 155809733115361, 2506135027165713, 42013633806350083, 732584456250306013, 13270900741926553641 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n)=n!*sum(k=1..n, sum(i=0..(n-k)/5, (-1)^i*binomial(k,k-i)*binomial(n-5*i-1,k-1))/k!), n>0, a(0)=1. E.g.f.: 1 + x*(E(0)-1)/(x+1) where E(k) =  1 + (1+x+x^2+x^3+x^4)/(k+1)/(1-x/(x+1/E(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 27 2013 PROG (Maxima) a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-5*i-1, k-1), i, 0, (n-k)/5)/k!, k, 1, n); CROSSREFS Sequence in context: A199317 A205776 A132846 * A193932 A193933 A000262 Adjacent sequences:  A193928 A193929 A193930 * A193932 A193933 A193934 KEYWORD nonn AUTHOR Vladimir Kruchinin, Aug 09 2011 STATUS approved

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