cp's OEIS Frontend

A367475 Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^3.

%I A367475 #11 Dec 04 2023 06:57:55
%S A367475 1,6,54,636,9204,157584,3111312,69533472,1734229344,47733263232,
%T A367475 1436801816448,46942939272960,1654215709835520,62533593070755840,
%U A367475 2524077593084160000,108339176213529384960,4927173048408858531840,236673892535088351744000
%N A367475 Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^3.
%F A367475 a(n) = (1/2) * Sum_{k=0..n} 2^k * (k+2)! * |Stirling1(n,k)|.
%F A367475 a(0) = 1; a(n) = 2*Sum_{k=1..n} (2*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k).
%p A367475 A367475 := proc(n)
%p A367475     option remember ;
%p A367475     if n =0 then
%p A367475         1;
%p A367475     else
%p A367475         2*add((2*k/n + 1) * (k-1)! * binomial(n,k) * procname(n-k),k=1..n) ;
%p A367475     end if;
%p A367475 end proc:
%p A367475 seq(A367475(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023
%o A367475 (PARI) a(n) = sum(k=0, n, 2^k*(k+2)!*abs(stirling(n, k, 1)))/2;
%Y A367475 Cf. A088500, A367474.
%Y A367475 Cf. A354122, A367471.
%K A367475 nonn
%O A367475 0,2
%A A367475 _Seiichi Manyama_, Nov 19 2023