A256182 G.f. A(x) satisfies: 1/A(x)^3 = Sum_{n>=0} (-1)^n * (1-7*n) * (-x)^(n*(n+1)/2).

1, 2, 8, 33, 152, 728, 3590, 18060, 92152, 475290, 2471985, 12943600, 68150321, 360491134, 1914406344, 10201142767, 54518961054, 292128744168, 1568916545308, 8443375819412, 45523087452426, 245849090689509, 1329718513219605, 7201896869193446, 39055252137506382, 212037592384217212

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..25.

Example

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

Prog

 (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)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A256183.

Sequence in context: A150886 A150887 A150888 * A030977 A030821 A236382

Adjacent sequences: A256179 A256180 A256181 * A256183 A256184 A256185

Keyword

nonn

Author

Paul D. Hanna, Mar 18 2015

Status

approved