login
G.f.: exp( Sum_{n>=1} A181411(n)*x^n/n ) where A181411(n) = Sum_{k=0..n} C(n,k)*sigma(n+k).
1

%I #2 Mar 30 2012 18:37:22

%S 1,4,17,65,234,804,2664,8571,26908,82721,249758,742178,2174623,

%T 6291982,17998815,50957814,142913510,397339309,1095887091,3000130003,

%U 8156568197,22032636494,59155443318,157925193036,419353166885,1107924552070

%N G.f.: exp( Sum_{n>=1} A181411(n)*x^n/n ) where A181411(n) = Sum_{k=0..n} C(n,k)*sigma(n+k).

%e G.f.: A(x) = 1 + 4*x + 17*x^2 + 65*x^3 + 234*x^4 + 804*x^5 +...

%e The logarithm of the g.f. begins:

%e log(A(x)) = 4*x + 18*x^2/2 + 55*x^3/3 + 150*x^4/4 + 379*x^5/5 + 915*x^6/6 + 2146*x^7/7 +...+ A181411(n)*x^n/n +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,sum(k=0,m,binomial(m,k)*sigma(m+k))*x^m/m)+x*O(x^n)),n)}

%Y Cf. A181411.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 19 2010