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A211825
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G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x) )^4.
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2
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1, 1, 8, 120, 2528, 66704, 2080128, 74115840, 2952926720, 129637843968, 6205231472640, 321275171444736, 17880710254829568, 1064356462925701120, 67476012302577762304, 4539384115900126199808, 323034928746773883518976, 24248087962137553507450880
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..17.
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FORMULA
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G.f. satisfies: A(x) = 1 + x*(A(x) + x*A'(x))^4.
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EXAMPLE
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G.f.: A(x) = 1 + x + 8*x^2 + 120*x^3 + 2528*x^4 + 66704*x^5 + 2080128*x^6 +...
Related expansions:
d/dx x*A(x) = 1 + 2*x + 24*x^2 + 480*x^3 + 12640*x^4 + 400224*x^5 +...
A'(x) = 1 + 16*x + 360*x^2 + 10112*x^3 + 333520*x^4 + 12480768*x^5 +...
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PROG
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*deriv(x*A)^4); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
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CROSSREFS
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Cf. A112915, A211824, A211826.
Sequence in context: A191098 A151834 A007762 * A113383 A218671 A045754
Adjacent sequences: A211822 A211823 A211824 * A211826 A211827 A211828
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Apr 21 2012
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STATUS
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approved
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