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A370533
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Expansion of g.f. A(x) satisfying A( x*(1 + 3*x)*A(x)^2 )^5 = A( x^2*(1 + 5*x)*A(x)^3 )^3.
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3
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1, 0, -15, 80, -255, 432, 1020, -12510, 71595, -354070, 1570104, -5622420, 13438045, -4035840, -135362385, 608528868, -646486560, -5733423180, 27001866935, 58064077890, -1517240012304, 12354566895940, -72313804557375, 336406302349200, -1168330262135925, 1853669275129548
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OFFSET
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1,3
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LINKS
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EXAMPLE
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G.f.: A(X) = x - 15*x^3 + 80*x^4 - 255*x^5 + 432*x^6 + 1020*x^7 - 12510*x^8 + 71595*x^9 - 354070*x^10 + 1570104*x^11 - 5622420*x^12 + ...
where A( x*(1 + 3*x)*A(x)^2 )^5 = A( x^2*(1 + 5*x)*A(x)^3 )^3.
RELATED SERIES.
B(x) = A( x*(1 + 3*x)*A^2 )^(1/3) = A( x^2*(1 + 5*x)*A(x)^3 )^(1/5)
where B(x) is the g.f. of A370534, which begins
B(x) = x + x^2 - 11*x^3 + 45*x^4 - 135*x^5 + 297*x^6 - 198*x^7 - 1872*x^8 + 15705*x^9 - 103695*x^10 + 556749*x^11 - 2275131*x^12 + 6904116*x^13 + ...
B(x)^3 = A( x*(1 + 3*x)*A(x)^2 ) = x^3 + 3*x^4 - 30*x^5 + 70*x^6 + 195*x^7 - 2391*x^8 + 11467*x^9 - 30645*x^10 + 11340*x^11 + 354870*x^12 + ...
B(x)^5 = A( x^2*(1 + 5*x)*A(x)^3 ) = x^5 + 5*x^6 - 45*x^7 + 15*x^8 + 1110*x^9 - 6354*x^10 + 12315*x^11 + 64365*x^12 - 658755*x^13 + 2858405*x^14 + ...
B(x)^15 = A( x*(1 + 3*x)*A(x)^2 )^5 = x^15 + 15*x^16 - 60*x^17 - 1180*x^18 + 6480*x^19 + 41688*x^20 - 480825*x^21 + 497475*x^22 + 16467975*x^23 + ...
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PROG
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(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); Ax = x*Ser(A);
A[#A] = polcoeff( subst(Ax, x, x^2*(1 + 5*x)*Ax^3 )^3 - subst(Ax, x, x*(1 + 3*x)*Ax^2 )^5, #A+14); ); A[n]}
for(n=1, 30, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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