%I #18 Nov 11 2020 19:40:40
%S 1,1,3,13,73,501,4051,37633,354033,3870793,46240291,597877941,
%T 8298856633,122751616573,1921371570483,31604885804521,552755907700321,
%U 10156326950561553,195421314725788483,3926668816722630493,82199760488718697641,1789438454541407131141
%N E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6+x^7).
%H Alois P. Heinz, <a href="/A193933/b193933.txt">Table of n, a(n) for n = 0..476</a>
%F E.g.f.: exp(Sum_{j=1..7} x^j).
%F a(n) = n!*sum(k=1..n, sum(i=0..(n-k)/7, (-1)^i*binomial(k,k-i)*binomial(n-7*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, 7)))
%p end:
%p seq(a(n), n=0..23); # _Alois P. Heinz_, Sep 29 2017
%t terms = 22;
%t CoefficientList[E^Total[x^Range[7]] + O[x]^terms, x] Range[0, terms-1]! (* _Jean-François Alcover_, Nov 11 2020 *)
%o (Maxima)
%o a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-7*i-1, k-1), i, 0, (n-k)/7)/k!, k, 1, n);
%o makelist(a(n),n,0,20);
%Y Column k=7 of A293669.
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Aug 09 2011