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A112938
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INVERT transform (with offset) of quadruple factorials (A008545), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^4]/A(x)^4.
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9
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1, 1, 4, 28, 292, 4156, 75844, 1694812, 44835172, 1369657468, 47422855300, 1834403141788, 78377228106148, 3664969183404220, 186134931067171012, 10201887125268108508, 600142156513333537252, 37713563573426417361148
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f. satisfies: A(x) = 1+x + 4*x^2*[d/dx A(x)]/A(x) (log derivative). G.f.: A(x) = 1+x +4*x^2/(1-7*x -4*2*3*x^2/(1-15*x -4*3*7*x^2/(1-23*x -4*4*11*x^2/(1-31*x -... -4*n*(4*n-5)*x^2/(1-(8*n-1)*x -...)))) (continued fraction). G.f.: A(x) = 1/(1-1*x/(1 -3*x/(1-4*x/(1 -7*x/(1-8*x/(1 -11*x/(1-12*x/(1 -...)))))))) (continued fraction).
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EXAMPLE
| A(x) = 1 + x + 4*x^2 + 28*x^3 + 292*x^4 + 4156*x^5 + ...
1/A(x) = 1 - x - 3*x^2 - 21*x^3 - 231*x^4 -... -A008545(n)*x^(n+1)-...
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PROG
| (PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+4*x^2*deriv(F)/F); return(polcoeff(F, n, x))}
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CROSSREFS
| Cf. A008545, A112939 (log derivative); A112934, A112935, A112936, A112937, A112940, A112941, A112942, A112943.
Sequence in context: A078634 A091485 A201354 * A007152 A177554 A192485
Adjacent sequences: A112935 A112936 A112937 * A112939 A112940 A112941
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 09 2005
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