cp's OEIS Frontend

A218120 G.f.: A(x) = exp( Sum_{n>=1} A069865(n)/2*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.

%I A218120 #7 Oct 13 2024 18:43:31
%S A218120 1,1,17,260,7244,214257,7593707,287419304,11745920475,503237634257,
%T A218120 22503750152879,1039694201489294,49401095274561608,
%U A218120 2402478324494963930,119201977436336120482,6017223412990713126034,308361587173800754305214,16013543997544827365960598
%N A218120 G.f.: A(x) = exp( Sum_{n>=1} A069865(n)/2*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.
%C A218120 Compare to a g.f. of Catalan numbers (A000108):
%C A218120 exp( Sum_{n>=1} A000984(n)/2*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.
%F A218120 Self-convolution equals A218119.
%e A218120 G.f.: A(x) = 1 + x + 17*x^2 + 260*x^3 + 7244*x^4 + 214257*x^5 + 7593707*x^6 +...
%e A218120 log(A(x)) = x + 33*x^2/2 + 730*x^3/3 + 27425*x^4/4 + 1015626*x^5/5 + 43437282*x^6/6 + 1924149396*x^7/7 +...+ A069865(n)/2*x^n/n +...
%o A218120 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^6)/2*x^m/m)+x*O(x^n)), n)}
%o A218120 for(n=0,25,print1(a(n),", "))
%Y A218120 Cf. A218119, A166991, A166993, A218118, A069865.
%K A218120 nonn
%O A218120 0,3
%A A218120 _Paul D. Hanna_, Oct 21 2012