cp's OEIS Frontend

A180719 Logarithmic derivative of A180718.

%I A180719 #2 Mar 30 2012 18:37:22
%S A180719 1,5,16,61,226,884,3543,14429,59623,248950,1049159,4454356,19032976,
%T A180719 81769735,352967821,1529948477,6655903632,29050257899,127162016206,
%U A180719 558088733406,2455157735151,10824115727199,47814658900427
%N A180719 Logarithmic derivative of A180718.
%F A180719 L.g.f.: L(x) = Sum_{n>=0} [ Sum_{k=0..n} C(n,k)^2*x^k ]^2*x^n/n.
%e A180719 L.g.f.: L(x) = x + 5*x^2/2 + 16*x^3/3 + 61*x^4/4 + 226*x^5/5 +...
%e A180719 which equals the sum of the series:
%e A180719 L(x) = (1 + x)^2*x
%e A180719 + (1 + 4*x + x^2)^2*x^2/2
%e A180719 + (1 + 9*x + 9*x^2 + x^3)^2*x^3/3
%e A180719 + (1 + 16*x + 36*x^2 + 16*x^3 + x^4)^2*x^4/4
%e A180719 + (1 + 25*x + 100*x^2 + 100*x^3 + 25*x^4 + x^5)^2*x^5/5
%e A180719 + (1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)^2*x^6/6 +...
%e A180719 where exponentiation yields the integer series:
%e A180719 exp(L(x)) = 1 + x + 3*x^2 + 8*x^3 + 25*x^4 + 80*x^5 + 271*x^6 + 952*x^7 + 3443*x^8 + 12758*x^9 + 48212*x^10 +...+ A180718(n)*x^n/n +...
%o A180719 (PARI) {a(n)=n*polcoeff(sum(m=1,n,sum(k=0,m,binomial(m,k)^2*x^k)^2*x^m/m)+x*O(x^n),n)}
%Y A180719 Cf. A180718.
%K A180719 nonn
%O A180719 1,2
%A A180719 _Paul D. Hanna_, Sep 24 2010