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EXAMPLE
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G.f.: A(x) = 1 + x - x^2 + 3*x^3 - 13*x^4 + 71*x^5 - 461*x^6 +-...
1/A(x) = 1 - x + 2*x^2 - 6*x^3 + 24*x^4 +...+ (-1)^n*n!*x^n +...
...
Coefficients of powers of g.f. A(x) begin:
A^1: 1,1,(-1),3,-13,71,-461,3447,-29093,273343,-2829325,...;
A^2: 1,2,(-1),(4),-19,110,-745,5752,-49775,476994,-5016069,...;
A^3: 1,3, 0, (4),(-21),129,-910,7242,-64155,626319,-6685548,...;
A^4: 1,4, 2, 4, (-21),(136),-996,8152,-73811,733244,-7938186,...;
A^5: 1,5, 5, 5, -20, (136),(-1030),8650,-79925,807055,-8854741,...;
A^6: 1,6, 9, 8, -18, 132, (-1030),(8856),-83385,855010,-9500385,...;
A^7: 1,7,14,14, -14, 126, -1008, (8856),(-84861),882805,-9927890,...;
A^8: 1,8,20,24, -6, 120, -972, 8712, (-84861),(894928),-10180120,...;
A^9: 1,9,27,39,9,117,-927,8469,-83772,(894928),(-10291986),...;
A^10:1,10,35,60,35,122,-875,8160,-81890,885620,(-10291986),...; ...
where coefficients [x^n] A(x)^n and [x^n] A(x)^(n-1) are
enclosed in parenthesis and equal (-1)^n*n*A075834(n+1):
[ -1,4,-21,136,-1030,8856,-84861,894928,-10291986,128165720,...];
[1,1,1,2,7,34,206,1476,12123,111866,1143554,12816572,...]
and also to the logarithmic derivative of A075834:
[1,1,4,21,136,1030,8856,84861,894928,10291986,128165720,...].
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