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A161968
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E.g.f. L(x) satisfies: L(x) = x*exp(x*d/dx L(x)), where L(x) is the logarithm of e.g.f. of A161967.
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3
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1, 2, 15, 232, 5905, 220176, 11210479, 743759360, 62179950753, 6387468716800, 790466735915791, 115974842104378368, 19906425428056709425, 3952505003715017695232, 899034956269244372091375, 232282033898506324396343296, 67660142460130946247667502401
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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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E.g.f. A(x), with offset=0, satisfies [Paul D. Hanna, Feb 15 2015]:
(1) A(x) = d/dx x*exp(x*A(x)).
(2) A(x) = exp(x*A(x)) * (1 + x*A(x) + x^2*A'(x)).
(3) exp(x*A(x)) = e.g.f. of A156326.
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EXAMPLE
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E.g.f.: L(x) = x + 2*x^2/2! + 15*x^3/3! + 232*x^4/4! + 5905*x^5/5! +...
where exp(L(x)) = exp(x*exp(x*L'(x))) = e.g.f. of A161967:
exp(L(x)) = 1 + x + 3*x^2/2! + 22*x^3/3! + 317*x^4/4! + 7596*x^5/5! +...
and exp(x*L'(x)) = 1 + x + 5*x^2/2! + 58*x^3/3! + 1181*x^4/4! + 36696*x^5/5! +...+ A156326(n)*x^n/n! +...
RELATED EXPRESSIONS.
E.g.f.: A(x) = 1 + 2*x + 15*x^2/2! + 232*x^3/3! + 5905*x^4/4! +...
where
A(x) = d/dx x*exp(x*A(x)) = exp(x*A(x)) * (1 + x*A(x) + x^2*A'(x)) with
exp(x*A(x)) = 1 + x + 5*x^2/2! + 58*x^3/3! + 1181*x^4/4! + 36696*x^5/5! + 1601497*x^6/6! + 92969920*x^7/7! +...+ A156326(n)*x^n/n! +...
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PROG
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(PARI) {a(n)=local(L=x+x^2); for(i=1, n, L=x*exp(x*deriv(L)+O(x^n))); n!*polcoeff(L, n)}
for(n=1, 30, 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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