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A256183
G.f. A(x) satisfies: 1/A(x)^3 = Sum_{n>=0} (-1)^n * (11*n+1) * x^(n*(n+1)/2).
1
1, 4, 32, 291, 2864, 29344, 308552, 3303000, 35827360, 392567622, 4336040577, 48205431920, 538811008877, 6049847821760, 68191652330640, 771200434566851, 8747162371041174, 99467000584413264, 1133643934300319998, 12946558434921516388, 148122965615855233266, 1697478425416109676039
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.
EXAMPLE
G.f.: A(x) = 1 + 4*x + 32*x^2 + 291*x^3 + 2864*x^4 + 29344*x^5 +...
where
1/A(x)^3 = 1 - 12*x + 23*x^3 - 34*x^6 + 45*x^10 - 56*x^15 + 67*x^21 - 78*x^28 + 89*x^36 - 100*x^45 + 111*x^55 +...+ (-1)^n*(11*n+1)*x^(n*(n+1)/2) +...
PROG
(PARI) {a(n)=local(A); A=sum(m=0, n, (-1)^m*(11*m+1)*x^(m*(m+1)/2) +x*O(x^n))^(-1/3); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Cf. A256182.
Sequence in context: A366663 A110901 A295538 * A000766 A370099 A267982
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 18 2015
STATUS
approved