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A090753
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Coefficients of power series A(x) such that n-th term of A(x)^n = n!*n*x^(n-1), for n>0.
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3
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1, 2, 2, 4, 16, 88, 600, 4800, 43680, 443296, 4949920, 60217408, 792134528, 11200176128, 169375195136, 2728019576832, 46626359376384, 842947307334144, 16073131554826752, 322403473258650624, 6786861273524305920
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OFFSET
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0,2
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COMMENTS
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At n=4 the 4th term of A(x)^4 is 4!*4x^3 = 96*x^3, as demonstrated by A(x)^4 = 1 + 8*x + 32*x^2 + 96*x^3 + 296*x^4 + ... See also A075834.
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LINKS
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FORMULA
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a(n) = Sum_{j=2..(n-2)} (j-1)*a(j)*a(n-j) for n>=2, with a(0)=1, a(1)=2.
G.f. satisfies: A(x) = 1 + 2*Sum_{n>=1} n^n * x^n / (A(x) + n*x)^n. - Paul D. Hanna, Feb 04 2013
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff(x/serreverse(sum(k=1, n+1, k!*x^k, x^2*O(x^n))), n)) /* Michael Somos, Feb 14 2004 */
(PARI) a(n)=local(A=1+x); for(i=1, n, A=1+2*sum(m=1, n, m^m*x^m/(A+m*x+x*O(x^n))^m)); polcoeff(A, n)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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