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Search: id:A136633
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| A136633 |
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G.f.: A(x) = Series_Reversion( x / Sum_{n>=0} (n+1)!*x^n ). |
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1
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| 1, 2, 10, 68, 544, 4832, 46312, 471536, 5055328, 56795840, 667286656, 8197599104, 105446118784, 1423627264256, 20234885027968, 303737480337152, 4827671316780544, 81385455480335360, 1455806861755411456
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f. A(x) satisifes: A(x) = F(x*A(x)) and A(x/F(x)) = F(x); a(n) = [x^n] F(x)^n / (n+1); where F(x) = Sum_{n>=0} (n+1)!*x^n.
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EXAMPLE
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G.f.: A(x) = 1 + 2x + 10x^2 + 68x^3 + 544x^4 + 4832x^5 + 46312x^6 +...
Let F(x) = 1 + 2x + 6x^2 + 24x^3 + 120x^4 + 720x^5 +...+ (n+1)!*x^n +...
then A(x) = F(x*A(x)) and A(x/F(x)) = F(x);
also, a(n) = coefficient of x^n in F(x)^n divided by (n+1).
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PROGRAM
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(PARI) a(n)=polcoeff(serreverse(x/sum(k=0, n, (k+1)!*x^k +x*O(x^n))), n)
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CROSSREFS
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Cf. A090753, A075834.
Sequence in context: A147725 A074603 A110520 this_sequence A082580 A136658 A104098
Adjacent sequences: A136630 A136631 A136632 this_sequence A136634 A136635 A136636
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 14 2008
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