cp's OEIS Frontend

A218119 G.f.: A(x) = exp( Sum_{n>=1} A069865(n)*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.

%I A218119 #7 Feb 01 2025 23:19:51
%S A218119 1,2,35,554,15297,451842,15929824,601077640,24488754772,1046792248856,
%T A218119 46718718597567,2155032002133834,102259392504591235,
%U A218119 4967499746642163574,246231868462969357492,12419324761881256326288,635990044563649443993091,33006906229799699591298070
%N A218119 G.f.: A(x) = exp( Sum_{n>=1} A069865(n)*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.
%C A218119 Compare to a g.f. of Catalan numbers (A000108):
%C A218119 exp( Sum_{n>=1} A000984(n)*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.
%F A218119 Equals row sums of triangle A218116.
%F A218119 Self-convolution of A218120.
%e A218119 G.f.: A(x) = 1 + 2*x + 35*x^2 + 554*x^3 + 15297*x^4 + 451842*x^5 + 15929824*x^6 +...
%e A218119 log(A(x)) = 2*x + 66*x^2/2 + 1460*x^3/3 + 54850*x^4/4 + 2031252*x^5/5 + 86874564*x^6/6 + 3848298792*x^7/7 +...+ A069865(n)*x^n/n +...
%o A218119 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^6)*x^m/m)+x*O(x^n)), n)}
%o A218119 for(n=0,25,print1(a(n),", "))
%Y A218119 Cf. A218116, A218120, A166990, A166992, A218117, A069865.
%K A218119 nonn
%O A218119 0,2
%A A218119 _Paul D. Hanna_, Oct 21 2012