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A295536
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G.f. A(x) satisfies: A(x) = 1 + x*A(x)^6 - x^2/A(x)^26.
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1
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1, 1, 5, 71, 375, 6682, 44580, 946312, 6922752, 145981865, 1096808573, 24010330078, 187616411332, 4183857848749, 33458964526535, 752695079265278, 6129198925216730, 139043863694798233, 1150329560451062383, 26226063866647040405, 219806629752765285995, 5027613613859350046965, 42619409376237650116405, 976900179567084519322460, 8365478066582587330962470
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OFFSET
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0,3
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COMMENTS
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Note that G(x) such that G(x) = 1 + x*G(x)^6 - x^2/G(x)^27 has negative coefficients.
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LINKS
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FORMULA
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G.f. A(x) satisfies: x^2 = A(x)^26 - A(x)^27 + x*A(x)^32.
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EXAMPLE
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G.f. A(x) = 1 + x + 5*x^2 + 71*x^3 + 375*x^4 + 6682*x^5 + 44580*x^6 + 946312*x^7 + 6922752*x^8 + 145981865*x^9 + 1096808573*x^10 + 24010330078*x^11 + 187616411332*x^12 + 4183857848749*x^13 + 33458964526535*x^14 + 752695079265278*x^15 +...
such that A(x) = 1 + x*A(x)^6 - x^2/A(x)^26.
RELATED SERIES.
A(x)^6 = 1 + 6*x + 45*x^2 + 596*x^3 + 5070*x^4 + 68058*x^5 + 674066*x^6 + 9948762*x^7 + 106491843*x^8 + 1599019100*x^9 +...
1/A(x)^26 = 1 - 26*x + 221*x^2 - 1612*x^3 + 23478*x^4 - 272246*x^5 + 3026010*x^6 - 39490022*x^7 + 502210527*x^8 +...
A(x)^26 = 1 + 26*x + 455*x^2 + 7696*x^3 + 117975*x^4 + 1761812*x^5 + 25510485*x^6 + 368086862*x^7 + 5245565832*x^8 +...
A(x)^27 = 1 + 27*x + 486*x^2 + 8352*x^3 + 130167*x^4 + 1967004*x^5 + 28797525*x^6 + 418814334*x^7 + 6013769832*x^8 +...
A(x)^32 = 1 + 32*x + 656*x^2 + 12192*x^3 + 205192*x^4 + 3287040*x^5 + 50727472*x^6 + 768204000*x^7 + 11445866084*x^8 +...
where x^2 = A(x)^26 - A(x)^27 + x*A(x)^32.
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A = 1 + x*A^6 - x^2/A^26 +x*O(x^n)); polcoeff(G=A, n)}
for(n=0, 40, 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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