cp's OEIS Frontend

A218117 G.f.: A(x) = exp( Sum_{n>=1} A005261(n)*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5.

%I A218117 #8 Oct 11 2024 16:11:18
%S A218117 1,2,19,198,2961,49566,938322,19083624,412160478,9305822076,
%T A218117 217855152321,5251363667622,129704365956114,3269927116717728,
%U A218117 83893626609970281,2185188966488265718,57673989852987800966,1539973309401567102832,41544812360973818992909
%N A218117 G.f.: A(x) = exp( Sum_{n>=1} A005261(n)*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5.
%C A218117 Compare to a g.f. of Catalan numbers (A000108):
%C A218117 exp( Sum_{n>=1} A000984(n)*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.
%F A218117 Equals row sums of triangle A218115.
%F A218117 Self-convolution of A218118.
%e A218117 G.f.: A(x) = 1 + 2*x + 19*x^2 + 198*x^3 + 2961*x^4 + 49566*x^5 + 938322*x^6 +...
%e A218117 log(A(x)) = 2*x + 34*x^2/2 + 488*x^3/3 + 9826*x^4/4 + 206252*x^5/5 + 4734304*x^6/6 + 113245568*x^7/7 +...+ A005261(n)*x^n/n +...
%o A218117 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^5)*x^m/m)+x*O(x^n)), n)}
%o A218117 for(n=0,25,print1(a(n),", "))
%Y A218117 Cf. A218115, A218118, A166990, A166992, A218119, A005261.
%K A218117 nonn
%O A218117 0,2
%A A218117 _Paul D. Hanna_, Oct 21 2012