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%I #12 Sep 29 2017 12:04:55
%S 1,1,3,13,73,501,4051,32593,313713,3326473,38377891,476464341,
%T 6299024953,87715975933,1314012177843,20776583119321,345267365639521,
%U 6009277853650833,109262845394221123,2073062512187103133,41084832105634595241,845645768972241105541
%N E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6).
%H Alois P. Heinz, <a href="/A193932/b193932.txt">Table of n, a(n) for n = 0..485</a>
%F a(n)=n!*sum(k=1..n, sum(i=0..(n-k)/6, (-1)^i*binomial(k,k-i)*binomial(n-6*i-1,k-1))/k!), n>0, a(0)=1.
%p a:= proc(n) option remember; `if`(n=0, 1, add(
%p a(n-j)*binomial(n-1, j-1)*j!, j=1..min(n, 6)))
%p end:
%p seq(a(n), n=0..23); # _Alois P. Heinz_, Sep 29 2017
%t With[{nn=20},CoefficientList[Series[Exp[Total[x^Range[6]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 12 2015 *)
%o (Maxima)
%o a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-6*i-1, k-1), i, 0, (n-k)/6)/k!, k, 1, n);
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Aug 09 2011
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