OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
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
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Aug 09 2011
STATUS
approved