A218118 - OEIS

%I #3 Oct 21 2012 10:36:45

%S 1,1,9,90,1350,22623,430338,8786367,190473510,4314088755,101271596421,

%T 2446843690671,60557118315384,1529356193511525,39297344717526330,

%U 1024958399339092751,27083985050402731646,723942169622258974974,19548657715769940178730

%N  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  Compare to a g.f. of Catalan numbers (A000108):

%C exp( Sum_{n>=1} A000984(n)/2*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.

%F  Self-convolution equals A218117.

%e  G.f.: A(x) = 1 + x + 9*x^2 + 90*x^3 + 1350*x^4 + 22623*x^5 + 430338*x^6 +...

%e 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  (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 for(n=0,25,print1(a(n),", "))

%Y  Cf. A218117, A166991, A166993, A218120, A005261.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 21 2012