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A161568
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E.g.f. satisfies: A(x) = exp(2*x*exp(3*x*A(x))).
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0
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1, 2, 16, 206, 3976, 101402, 3237220, 124293206, 5582747824, 287346080690, 16680250440124, 1078327289938670, 76840445565238024, 5984507179839282122, 505778795448930860308, 46104043794638089809158
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = Sum_{k=0..n} C(n,k) * 2^k * 3^(n-k) * (n-k+1)^(k-1) * k^(n-k).
More generally, if G(x) = exp(p*x*exp(q*x*G(x))) = Sum_{n>=0} g(n)*x^n/n!,
then g(n) = Sum_{k=0..n} C(n,k) * p^k * q^(n-k) * (n-k+1)^(k-1) * k^(n-k).
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EXAMPLE
| E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 206*x^3/3! + 3976*x^4/4! +...
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PROG
| (PARI) {a(n)=sum(k=0, n, binomial(n, k)*2^k*3^(n-k)*(n-k+1)^(k-1)*k^(n-k))}
(PARI) {a(n)=local(A=1+x); for(i=0, n, A=exp(2*x*exp(3*x*A+O(x^n)))); n!*polcoeff(A, n, x)}
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CROSSREFS
| Cf. A161565, A161566, A161567.
Sequence in context: A012677 A158212 A036081 * A138429 A087923 A004121
Adjacent sequences: A161565 A161566 A161567 * A161569 A161570 A161571
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 14 2009
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