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A219359
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G.f. satisfies: A(x) = Sum_{n>=0} n! * x^n * A(x)^(n*(n+1)/2).
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3
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1, 1, 3, 15, 99, 785, 7151, 73097, 827501, 10295549, 140100323, 2077648871, 33466994639, 583535328293, 10971899911703, 221571516903233, 4786126571515961, 110142864494603313, 2690257065904106571, 69500954207702580927, 1893141166438848208747, 54217997416999007587201
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f. satisfies: A(x) = B(x*A(x)) and A(x/B(x)) = B(x) where B(x) satisfies:
B(x) = Sum_{n>=0} n!*x^n * B(x)^(n*(n-1)/2) and is the g.f. of A219358.
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 99*x^4 + 785*x^5 + 7151*x^6 +...
where
A(x) = 1 + 1!*x*A(x) + 2!*x^2*A(x)^3 + 3!*x^3*A(x)^6 + 4!*x^4*A(x)^10 + 5!*x^5*A(x)^15 +...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, k!*x^k*(A+x*O(x^n))^(k*(k+1)/2))); polcoeff(A, n)}
for(n=0, 25, print1(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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