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A218224
G.f. A(x) satisfies: A(x) = 1+x + x^2*[d/dx A(x)^4].
3
1, 1, 4, 44, 684, 13636, 328000, 9198240, 294075040, 10549834368, 419626384128, 18330935118080, 872618259925632, 44970631837229184, 2494887017741434368, 148272655438005392896, 9399158287979230003200, 633107847492164526284800, 45159576693655485274008576
OFFSET
0,3
LINKS
FORMULA
G.f. A(x) satisfies: A(x) = 1+x + 4*x^2*A(x)^3*A'(x).
a(n) ~ c * 4^n * n! / n^(1/4), where c = 0.2277218505566340305314... - Vaclav Kotesovec, Aug 24 2017
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 44*x^3 + 684*x^4 + 13636*x^5 + 328000*x^6 +...
Related series:
A(x)^3 = 1 + 4*x + 22*x^2 + 228*x^3 + 3409*x^4 + 65600*x^5 + 1533040*x^6 +...
d/dx A(x)^3 = 4 + 44*x + 684*x^2 + 13636*x^3 + 328000*x^4 + 9198240*x^5 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x+x^2*deriv(A^4+x*O(x^n))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Sequence in context: A103870 A371680 A056063 * A177749 A291198 A053332
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 23 2012
STATUS
approved