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A221413
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O.g.f. satisfies: A(x) = Sum_{n>=0} (n+4)^n * x^n * A(n*x)^n/n! * exp(-(n+4)*x*A(n*x)).
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6
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1, 1, 6, 53, 931, 21847, 791525, 39781921, 2896348222, 298603689072, 43979877929712, 9234821696038425, 2765498896234870783, 1182132922860352133076, 721128788569371093881079, 628104461090874688307332589, 781298529318782688558174387547
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OFFSET
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0,3
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LINKS
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EXAMPLE
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O.g.f.: A(x) = 1 + x + 6*x^2 + 53*x^3 + 931*x^4 + 21847*x^5 + 791525*x^6 +...
where
A(x) = exp(-4*x) + 5*x*A(x)*exp(-5*x*A(x)) + 6^2*x^2*A(2*x)^2/2!*exp(-6*x*A(2*x)) + 7^3*x^3*A(3*x)^3/3!*exp(-7*x*A(3*x)) + 8^4*x^4*A(4*x)^4/4!*exp(-8*x*A(4*x)) + 9^5*x^5*A(5*x)^5/5!*exp(-9*x*A(5*x)) +...
simplifies to a power series in x with integer coefficients.
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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+4)^k*x^k*subst(A, x, k*x)^k/k!*exp(-(k+4)*x*subst(A, x, k*x)+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 20, 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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