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A217989
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G.f. satisfies: A(x) = 1+x + x^2*A'(x)*A(x)^2.
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1
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1, 1, 1, 4, 19, 116, 835, 6890, 63826, 654552, 7354893, 89830770, 1184915556, 16788863356, 254342837905, 4103256660048, 70241858430220, 1271839899568064, 24287699718766932, 487891841580468294, 10285169201486942788, 227042177973572054900
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) ~ c * n! * n, where c = 0.21362630601338471861707529847387... - Vaclav Kotesovec, Feb 22 2014
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + 4*x^3 + 19*x^4 + 116*x^5 + 835*x^6 + 6890*x^7 +...
Related expansions:
A'(x) = 1 + 2*x + 12*x^2 + 76*x^3 + 580*x^4 + 5010*x^5 + 48230*x^6 +...
A(x)^2 = 1 + 2*x + 3*x^2 + 10*x^3 + 47*x^4 + 278*x^5 + 1956*x^6 + 15834*x^7 +...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x+x^2*A'*(A^2+x*O(x^n))); polcoeff(A, n)}
for(n=0, 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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