cp's OEIS Frontend

A369751 Expansion of e.g.f. exp(1 - (1+x)^3).

%I A369751 #12 Feb 02 2024 14:48:34
%S A369751 1,-3,3,21,-63,-423,1899,15201,-72063,-832491,3105459,60090093,
%T A369751 -110508543,-5224722831,-3828328677,510699368313,2104026859521,
%U A369751 -52582823289171,-473592954347037,5168227121231301,92434892126557761,-357595962971807223,-17085974691782295477
%N A369751 Expansion of e.g.f. exp(1 - (1+x)^3).
%F A369751 a(0) = 1; a(n) = -3 * (n-1)! * Sum_{k=1..min(3,n)} binomial(2,k-1) * a(n-k)/(n-k)!.
%F A369751 a(n) = Sum_{k=0..n} 3^k * Stirling1(n,k) * A000587(k).
%F A369751 D-finite with recurrence a(n) +3*a(n-1) +6*(n-1)*a(n-2) +3*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Feb 02 2024
%p A369751 A369751 := proc(n)
%p A369751     option remember ;
%p A369751     if n =0 then
%p A369751         1;
%p A369751     else
%p A369751         add( binomial(2,k-1) * procname(n-k)/(n-k)!,k=1..min(3,n)) ;
%p A369751         -3*(n-1)!*% ;
%p A369751     end if;
%p A369751 end proc:
%p A369751 seq(A369751(n),n=0..20) ; # _R. J. Mathar_, Feb 02 2024
%o A369751 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-(1+x)^3)))
%Y A369751 Column k=3 of A369738.
%Y A369751 Cf. A000587, A192989.
%K A369751 sign
%O A369751 0,2
%A A369751 _Seiichi Manyama_, Jan 30 2024