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A369534
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G.f. A(x) satisfies: A( 4*A(x)^4 - 64*A(x)^5 ) = 4*x^4.
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5
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1, 4, 56, 1024, 21212, 473056, 11074656, 268419072, 6677240840, 169503014016, 4373238900672, 114340618960896, 3022828138341280, 80668863489274880, 2170196738706696448, 58793507835449704448, 1602579845950784683616, 43919681465696136388608, 1209451899880085285430528
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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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G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
(1) A( 4*A(x)^4 - 64*A(x)^5 ) = 4*x^4.
(2) A( ( A(4*x^4 - 64*x^5)/4 )^(1/4) ) = x.
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EXAMPLE
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G.f.: A(x) = x + 4*x^2 + 56*x^3 + 1024*x^4 + 21212*x^5 + 473056*x^6 + 11074656*x^7 + 268419072*x^8 + 6677240840*x^9 + 169503014016*x^10 + ...
RELATED SERIES.
4*A(x)^4 - 64*A(x)^5 = 4*x^4 - 64*x^8 - 1536*x^12 - 57344*x^16 - 2519040*x^20 - 121438208*x^24 - 6133645312*x^28 - ...
where A( 4*A(x)^4 - 64*A(x)^5 ) = 4*x^4.
Let B(x) satisfy A(B(x)) = B(A(x)) = x, where
B(x) = x - 4*x^2 - 24*x^3 - 224*x^4 - 2460*x^5 - 29648*x^6 - 374368*x^7 - 4921728*x^8 - 66447288*x^9 - ...
then B(x)^4 = A(4*x^4 - 64*x^5)/4 which begins
B(x)^4 = x^4 - 16*x^5 + 16*x^8 - 512*x^9 + 4096*x^10 + 896*x^12 - 43008*x^13 + 688128*x^14 - 3670016*x^15 + 65536*x^16 + ...
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PROG
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(PARI) {a(n) = my(V=[1]); for(i=1, n, V=concat(V, 0); A = x*Ser(V); V[#V] = -polcoeff(subst(G=A, x, 4*A^4 - 64*A^5 ), #V+3)/16); V[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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