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A112936
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INVERT transform (with offset) of triple factorials (A008544), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^3]/A(x)^3.
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9
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1, 1, 3, 15, 111, 1131, 14943, 243915, 4742391, 106912131, 2739347103, 78569371275, 2492748594471, 86650852740531, 3274367635513263, 133625238021647835, 5856377114106629751, 274320168321004350531
(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 + 3*x^2*[d/dx A(x)]/A(x) (log derivative). G.f.: A(x) = 1+x +3*x^2/(1-5*x -3*2*2*x^2/(1-11*x -3*3*5*x^2/(1-17*x -3*4*8*x^2/(1-23*x -... -3*n*(3*n-4)*x^2/(1-(6*n-1)*x -...)))) (continued fraction). G.f.: A(x) = 1/(1-x/(1 -2*x/(1-3*x/(1 -5*x/(1-6*x/(1 -8*x/(1-9*x/(1 -...)))))))) (continued fraction).
a(n) = (3*n - 2) * a(n-1) - Sum_{k=1..n-1} a(k) * a(n-k) if n>1. - Michael Somos, Jul 23 2011
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EXAMPLE
| A(x) = 1 + x + 3*x^2 + 15*x^3 + 111*x^4 + 1131*x^5 + 14943*x^6 +...
1/A(x) = 1 - x - 2*x^2 - 10*x^3 - 80*x^4 - 880*x^5 -...-A008544(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+3*x^2*deriv(F)/F); return(polcoeff(F, n, x))}
(PARI) {a(n) = local(A); if( n<1, n==0, A = vector(n); A[1] = 1; for( k=2, n, A[k] = (3*k - 2) * A[k-1] - sum( j=1, k-1, A[j] * A[k-j])); A[n])} /* Michael Somos, Jul 23 2011 */
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CROSSREFS
| Cf. A008544, A112937 (log derivative); A112934, A112935, A112938, A112939, A112940, A112941, A112942, A112943.
Sequence in context: A109498 A142967 A201339 * A001063 A130168 A089945
Adjacent sequences: A112933 A112934 A112935 * A112937 A112938 A112939
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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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