cp's OEIS Frontend

A168268 G.f.: exp( Sum_{n>=1} A007837(n)*x^n/n ), where A007837(n) = number of partitions of n-set with distinct block sizes.

%I A168268 #14 Mar 18 2022 07:38:30
%S A168268 1,1,1,2,3,6,20,45,116,385,2224,6396,23708,88065,445784,3962502,
%T A168268 14478825,64495508,309085415,1608099881,10856426344,142802148953,
%U A168268 604464533847,3324499738872,17795211310951,112537384959231,718232376832560
%N A168268 G.f.: exp( Sum_{n>=1} A007837(n)*x^n/n ), where A007837(n) = number of partitions of n-set with distinct block sizes.
%C A168268 Conjectured to consist entirely of integers.
%e A168268 G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 20*x^6 + 45*x^7 +...
%e A168268 log(A(x)) = x + x^2/2 + 4*x^3/3 + 5*x^4/4 + 16*x^5/5 + 82*x^6/6 + 169*x^7/7 + 541*x^8/8 +...+ A007837(n)*x^n/n +...
%o A168268 (PARI) {a(n)=polcoeff(exp(serlaplace(intformal((-1+prod(k=1, n+1, 1+x^k/k! +x^2*O(x^n)))/x))), n)}
%Y A168268 Cf. A007837.
%K A168268 nonn
%O A168268 0,4
%A A168268 _Paul D. Hanna_, Jan 05 2011