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Search: id:A161566
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| A161566 |
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E.g.f. satisfies: A(x) = exp(2*x*exp(x*A(x))). |
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+0
5
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| 1, 2, 8, 62, 696, 10362, 193036, 4323846, 113288720, 3401106290, 115150465044, 4341507224958, 180422159478424, 8194551731190762, 403871802897954332, 21468380724070186358, 1224364515329753354784, 74574475891799118725346
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OFFSET
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0,2
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FORMULA
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a(n) = Sum_{k=0..n} 2^k * C(n,k) * (n-k+1)^(k-1) * k^(n-k).
E.g.f.: A(x) = B(x)^2 where B(x) = e.g.f. of A161567.
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EXAMPLE
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E.g.f.: A(x) = 1 + 2*x + 8*x^2/2! + 62*x^3/3! + 696*x^4/4! +...
log(A(x)) = 2*x*C(x) where C(x) = exp(x*A(x)) = e.g.f. of A161565:
C(x) = 1 + x + 5*x^2/2! + 37*x^3/3! + 417*x^4/4! + 6201*x^5/5! +...
A(x)^(1/2) = e.g.f. of A161567:
A(x)^(1/2) = 1 + x + 3*x^2/2! + 22*x^3/3! + 233*x^4/4! + 3356*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, 2^k*binomial(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(x*A+O(x^n)))); n!*polcoeff(A, n, x)}
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CROSSREFS
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Cf. A161565, A161567.
Sequence in context: A116976 A132574 A086903 this_sequence A159476 A006245 A009271
Adjacent sequences: A161563 A161564 A161565 this_sequence A161567 A161568 A161569
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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), Jun 14 2009
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