A228648 - OEIS

%I #11 Aug 28 2013 23:32:58

%S 1,1,3,13,128,2974,161048,19632276,5284440413,3112165670205,

%T 3990553641147871,11107142249379896577,66971338268043285905138,

%U 873496931276771661395863398,24617613776054408956962658439353,1497874647146694311608664496205734267,196633628592570082430451891781759097556806

%N G.f.: exp( Sum_{n>=1} A001609(n^2)*x^n/n ), where the l.g.f. of A001609 is -log(1-x-x^3).

%C A001609 forms the logarithmic derivative of Narayana's cows sequence A000930.

%F Logarithmic derivative yields A228647.

%e G.f.: A(x) = 1 + x + 3*x^2 + 13*x^3 + 128*x^4 + 2974*x^5 + 161048*x^6 +...

%e where

%e log(A(x)) = x + 5*x^2/2 + 31*x^3/3 + 453*x^4/4 + 14131*x^5/5 + 946781*x^6/6 + 136250983*x^7/7 +...+ A001609(n^2)*x^n/n +...

%o (PARI) {A001609(n)=n*polcoeff(-log(1-x-x^3 +x*O(x^n)), n)}

%o {a(n)=polcoeff(exp(sum(m=1,n+1,A001609(m^2)*x^m/m)+x*O(x^n)),n)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A228647, A001609, A000930.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 28 2013