A256182 - OEIS

%I #4 Mar 18 2015 22:40:13

%S 1,2,8,33,152,728,3590,18060,92152,475290,2471985,12943600,68150321,

%T 360491134,1914406344,10201142767,54518961054,292128744168,

%U 1568916545308,8443375819412,45523087452426,245849090689509,1329718513219605,7201896869193446,39055252137506382,212037592384217212

%N  G.f. A(x) satisfies: 1/A(x)^3 = Sum_{n>=0} (-1)^n * (1-7*n) * (-x)^(n*(n+1)/2).

%C  Compare to: 1/P(x)^3 = Sum_{n>=0} (-1)^n * (2*n+1) * x^(n*(n+1)/2), where P(x) is the partition function of A000041.

%e  G.f.: A(x) = 1 + 2*x + 8*x^2 + 33*x^3 + 152*x^4 + 728*x^5 + 3590*x^6 +...

%e where

%e 1/A(x)^3 = 1 - 6*x + 13*x^3 + 20*x^6 - 27*x^10 - 34*x^15 + 41*x^21 + 48*x^28 - 55*x^36 - 62*x^45 + 69*x^55 +...+ (-1)^n*(1-7*n)*(-x)^(n*(n+1)/2) +...

%o  (PARI) {a(n)=local(A);A=sum(m=0,n,(-1)^m*(1-7*m)*(-x)^(m*(m+1)/2) +x*O(x^n))^(-1/3); polcoeff(A,n)}

%o for(n=0,30,print1(a(n),", "))

%Y  Cf. A256183.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 18 2015