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%I #7 Jan 13 2018 04:41:20
%S 1,1,3,31,112,1223,5114,66329,316312,4173481,20940941,277101696,
%T 1446481076,19319116495,104511172380,1397657888918,7778128795060,
%U 103740888802178,591475611993653,7858075292945250,45784070752763376,605149066777845111,3595295341839184400,47234806041386608505,285674893498876513412,3728641722675490266822,22925358764925173689433,297162459818038867739176
%N G.f. A(x) satisfies: A(x) = 1 + x*A(x)^4 - x^2/A(x)^13.
%C Note that G(x) such that G(x) = 1 + x*G(x)^4 - x^2/G(x)^14 has negative coefficients.
%H Paul D. Hanna, <a href="/A295534/b295534.txt">Table of n, a(n) for n = 0..500</a>
%F G.f. A(x) satisfies: x^2 = A(x)^13 - A(x)^14 + x*A(x)^17.
%e G.f. A(x) = 1 + x + 3*x^2 + 31*x^3 + 112*x^4 + 1223*x^5 + 5114*x^6 + 66329*x^7 + 316312*x^8 + 4173481*x^9 + 20940941*x^10 + 277101696*x^11 + 1446481076*x^12 + 19319116495*x^13 + 104511172380*x^14 + 1397657888918*x^15 +...
%e such that A(x) = 1 + x*A(x)^4 - x^2/A(x)^13.
%e RELATED SERIES.
%e A(x)^4 = 1 + 4*x + 18*x^2 + 164*x^3 + 911*x^4 + 7844*x^5 + 48792*x^6 + 451668*x^7 + 3073083*x^8 + 29305648*x^9 + 207988496*x^10 +...
%e 1/A(x)^13 = 1 - 13*x + 52*x^2 - 312*x^3 + 2730*x^4 - 17537*x^5 + 135356*x^6 - 1100398*x^7 + 8364707*x^8 - 69113200*x^9 + 559529048*x^10 +...
%e A(x)^13 = 1 + 13*x + 117*x^2 + 1157*x^3 + 10283*x^4 + 92066*x^5 + 796341*x^6 + 7007286*x^7 + 60731112*x^8 + 535088450*x^9 + 4666522341*x^10 +...
%e A(x)^14 = 1 + 14*x + 133*x^2 + 1344*x^3 + 12306*x^4 + 112126*x^5 + 989240*x^6 + 8804084*x^7 + 77325101*x^8 + 686378420*x^9 + 6044351516*x^10 +...
%e A(x)^17 = 1 + 17*x + 187*x^2 + 2023*x^3 + 20060*x^4 + 192899*x^5 + 1796798*x^6 + 16593989*x^7 + 151289970*x^8 + 1377829175*x^9 + 12469684059*x^10 +...
%e where x^2 = A(x)^13 - A(x)^14 + x*A(x)^17.
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A = 1 + x*A^4 - x^2/A^13 +x*O(x^n)); polcoeff(G=A, n)}
%o for(n=0, 40, print1(a(n), ", "))
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 23 2017
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