cp's OEIS Frontend

A218118 G.f.: A(x) = exp( Sum_{n>=1} A005261(n)/2*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5.

%I A218118 #6 Aug 06 2025 22:36:51
%S A218118 1,1,9,90,1350,22623,430338,8786367,190473510,4314088755,101271596421,
%T A218118 2446843690671,60557118315384,1529356193511525,39297344717526330,
%U A218118 1024958399339092751,27083985050402731646,723942169622258974974,19548657715769940178730
%N A218118 G.f.: A(x) = exp( Sum_{n>=1} A005261(n)/2*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5.
%C A218118 Compare to a g.f. of Catalan numbers (A000108):
%C A218118 exp( Sum_{n>=1} A000984(n)/2*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.
%F A218118 Self-convolution equals A218117.
%e A218118 G.f.: A(x) = 1 + x + 9*x^2 + 90*x^3 + 1350*x^4 + 22623*x^5 + 430338*x^6 +...
%e A218118 log(A(x)) = x + 17*x^2/2 + 244*x^3/3 + 4913*x^4/4 + 103126*x^5/5 + 2367152*x^6/6 + 56622784*x^7/7 +...+ A005261(n)/2*x^n/n +...
%o A218118 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^5)/2*x^m/m)+x*O(x^n)), n)}
%o A218118 for(n=0,25,print1(a(n),", "))
%Y A218118 Cf. A218117, A166991, A166993, A218120, A005261.
%K A218118 nonn
%O A218118 0,3
%A A218118 _Paul D. Hanna_, Oct 21 2012