OFFSET
0,5
COMMENTS
EXAMPLE
G.f.: A(x) = 1 + x - x^2 + x^3 - 7*x^4 - 49*x^5 - 1191*x^6 - 31569*x^7 -...
Coefficients of x^k in the powers A(x)^(n^2-n+1) of g.f. A(x) begin:
n=1: [1, 1, -1, 1, -7, -49, -1191, -31569, -1051695, ...];
n=2: [1, 3, 0, -2, -15, -189, -3850, -101700, -3340845, ...];
n=3: [1, 7, 14, 0, -56, -588, -10808, -273972, -8760325, ...];
n=4: [1,13, 65, 143, 0, -1742, -27534, -638690, -19496334, ...];
n=5: [1,21, 189, 931, 2478, 0, -67312, -1444608, -40653711, ...];
n=6: [1,31, 434, 3596, 19158, 62062, 0, -3116120, -84939504, ...];
n=7: [1,43, 860,10578, 88795, 526449, 2045854, 0,-167991196, ...];
n=8: [1,57,1539,26125,311619,2754297,18283187, 83718693, 0, ...];
...
where the coefficients of x^n in A(x)^(n^2-n+1) all equal zero for n>=2.
PROG
(PARI) {a(n)=local(A=[1, 1]); for(k=1, n, A=concat(A, 0); A[#A]=-polcoeff((Ser(A) +O(x^(k+2)))^(k^2+k+1)/(k^2+k+1), k+1)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 14 2013
STATUS
approved