cp's OEIS Frontend

A224976 L.g.f.: log( 1 + Sum_{n>=1} x^(n*(3*n-1)/2) + x^(n*(3*n+1)/2) ) = Sum_{n>=1} a(n)*x^n/n.

%I A224976 #12 Apr 21 2013 21:25:05
%S A224976 1,1,-2,1,6,-8,8,1,-11,6,12,-20,14,8,-12,1,18,-35,20,6,-16,12,24,-44,
%T A224976 31,14,-38,8,30,-48,32,1,-24,18,48,-83,38,20,-28,6,42,-64,44,12,-66,
%U A224976 24,48,-92,57,31,-36,14,54,-116,72,8,-40,30,60,-120,62,32,-88,1,84,-96,68,18,-48,48,72
%N A224976 L.g.f.: log( 1 + Sum_{n>=1} x^(n*(3*n-1)/2) + x^(n*(3*n+1)/2) ) = Sum_{n>=1} a(n)*x^n/n.
%C A224976 Compare to: -log( 1 + Sum_{n>=1} (-1)^n*(x^(n*(3*n-1)/2) + x^(n*(3*n+1)/2)) ) = Sum_{n>=1} sigma(n)*x^n/n.
%H A224976 Paul D. Hanna, <a href="/A224976/b224976.txt">Table of n, a(n) for n = 1..10000</a>
%F A224976 a(n) = 2*A111932(n) - sigma(n), where sigma(n) is the sum of divisors of n.
%F A224976 a(n) = 1 iff n = 2^k for k>=0.
%F A224976 L.g.f.: log(1 + Sum_{n>=1} x^A001318(n)) = Sum_{n>=1} a(n)*x^n/n, where A001318 are the generalized pentagonal numbers.
%e A224976 L.g.f.: A(x) = x + x^2/2 - 2*x^3/3 + x^4/4 + 6*x^5/5 - 8*x^6/6 + 8*x^7/7 + x^8/8 - 11*x^9/9 + 6*x^10/10 + 12*x^11/11 - 20*x^12/12 +...
%e A224976 where
%e A224976 exp(A(x)) = 1 + x + x^2 + x^5 + x^7 + x^12 + x^15 + x^22 + x^26 + x^35 + x^40 + x^51 + x^57 + x^70 + x^77 +...+ x^A001318(n) +...
%o A224976 (PARI) {a(n)=n*polcoeff(log(1+sum(k=1,n,x^(k*(3*k-1)/2) + x^(k*(3*k+1)/2))+x*O(x^n)),n)}
%o A224976 for(n=1,80,print1(a(n),", "))
%Y A224976 Cf. A111932, A001318, A000203 (sigma).
%K A224976 sign
%O A224976 1,3
%A A224976 _Paul D. Hanna_, Apr 21 2013