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A161567
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E.g.f. satisfies: A(x) = exp(x*exp(x*A(x)^2)).
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4
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1, 1, 3, 22, 233, 3356, 61057, 1343686, 34731377, 1031493880, 34617603041, 1295705404874, 53516386593001, 2417918198462404, 118628419305036929, 6280926119941402486, 356960234149564116833, 21674784895404653181680
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k=0..n} C(n,k) * (2*(n-k) + 1)^(k-1) * k^(n-k).
E.g.f.: A(x) = F(x)^(1/2) where F(x) = e.g.f. of A161566.
E.g.f.: A(x) = exp(x*G(x)) where G(x) = e.g.f. of A161565.
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EXAMPLE
| E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 233*x^4/4! +...
log(A(x)) = x*G(x) where G(x) = exp(x*A(x)^2) = e.g.f. of A161565:
G(x) = 1 + x + 5*x^2/2! + 37*x^3/3! + 417*x^4/4! + 6201*x^5/5! +...
A(x)^2 = e.g.f. of A161566:
A(x)^2 = 1 + 2*x + 8*x^2/2! + 62*x^3/3! + 696*x^4/4! + 10362*x^5/5! +...
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PROG
| (PARI) {a(n)=sum(k=0, n, binomial(n, k)*(2*(n-k)+1)^(k-1)*k^(n-k))}
(PARI) {a(n)=local(A=1+x); for(i=0, n, A=exp(x*exp(x*A^2+O(x^n)))); n!*polcoeff(A, n, x)}
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CROSSREFS
| Cf. A161565, A161566.
Sequence in context: A073530 A120667 A196958 * A141006 A042703 A141356
Adjacent sequences: A161564 A161565 A161566 * A161568 A161569 A161570
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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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