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A193160
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E.g.f. A(x) satisfies: A(x/(1-x)) = x*A'(x).
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1
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1, 2, 9, 68, 760, 11664, 233828, 5905696, 182846592, 6792372480, 297550188672, 15153482847744, 886517886778368, 58975120009537536, 4422337095720648960, 370957479138591903744, 34576037926690499493888, 3559813114275891217760256
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = n*(n-2)!* Sum_{k=1..n-1} C(n-1,k-1)* a(k)/k! for n>1 with a(1)=1.
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EXAMPLE
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E.g.f.: A(x) = x + 2*x^2/2! + 9*x^3/3! + 68*x^4/4! + 760*x^5/5! +...
Related expansions:
A(x/(1-x)) = x + 4*x^2/2! + 27*x^3/3! + 272*x^4/4! + 3800*x^5/5! +...
x*A'(x) = x + 4*x^2/2! + 27*x^3/3! + 272*x^4/4! + 3800*x^5/5! +...
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PROG
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(PARI) {a(n)=local(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A]=Vec(subst(F, x, x/(1-x)))[#A]/(#A-1)); if(n<1, 0, n!*A[n])}
(PARI) {a(n)=if(n<1, 0, if(n==1, 1, n!/(n-1)*sum(k=1, n-1, binomial(n-1, k-1)*a(k)/k!)))}
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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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