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A193931
E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5).
3
1, 1, 3, 13, 73, 501, 3331, 27553, 253233, 2540233, 27340291, 309811701, 3843476473, 50560182973, 701098196163, 10205952248521, 155809733115361, 2506135027165713, 42013633806350083, 732584456250306013, 13270900741926553641, 249625454707702681861
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
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*binomial(n-1, j-1)*j!, j=1..min(n, 5)))
end:
seq(a(n), n=0..23); # Alois P. Heinz, Sep 29 2017
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: A205776 A132846 A293196 * A367757 A293197 A193932
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Aug 09 2011
STATUS
approved