cp's OEIS Frontend

A198892 E.g.f.: 1/[ Sum_{n>=0} (-x)^(n*(n+1)/2) / A000178(n) ] where A000178(n) = Product_{k=1..n} k!.

%I A198892 #9 Aug 27 2023 13:58:55
%S A198892 1,1,2,9,48,300,2280,20580,211680,2434320,31134600,438807600,
%T A198892 6744276000,112237725600,2011760150400,38639999197800,791610365145600,
%U A198892 17230493212732800,397111119429024000,9660782144094681600,247393077222459168000,6651976858409613931200
%N A198892 E.g.f.: 1/[ Sum_{n>=0} (-x)^(n*(n+1)/2) / A000178(n) ] where A000178(n) = Product_{k=1..n} k!.
%e A198892 E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 48*x^4/4! + 300*x^5/5! +...
%e A198892 where
%e A198892 1/A(x) = 1 - x/1! - x^3/(1!*2!) + x^6/(1!*2!*3!) + x^10/(1!*2!*3!*4!) - x^15/(1!*2!*3!*4!*5!) - x^21/(1!*2!*3!*4!*5!*6!) ++--...
%e A198892 1/A(x) = 1 - x - x^3/2 + x^6/12 + x^10/288 - x^15/34560 - x^21/24883200 +...
%o A198892 (PARI) {a(n) = my(A=1/sum(m=0,sqrtint(2*n+1), (-x)^(m*(m+1)/2) / prod(k=1,m,k!)+x*O(x^n))); n!*polcoeff(A,n)}
%o A198892 for(n=0,25,print1(a(n),", "))
%Y A198892 Cf. A198891.
%K A198892 nonn
%O A198892 0,3
%A A198892 _Paul D. Hanna_, Oct 30 2011