A295533 G.f. A(x) satisfies: A(x) = 1 + x*A(x)^3 - x^2/A(x)^7.

1, 1, 2, 16, 47, 339, 1166, 8976, 35651, 278278, 1212177, 9302196, 43167236, 325489466, 1589818896, 11803540132, 60156687345, 440114954611, 2323481492945, 16768350745596, 91184229198927, 650047467387705, 3625017748598077, 25563565222047060, 145663567184376470, 1017461783465817794, 5906152744555574559, 40912038149899432252, 241322973993725872166

Offset

0,3

Comments

Note that G(x) such that G(x) = 1 + x*G(x)^3 - x^2/G(x)^8 has negative coefficients.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Formula

G.f. A(x) satisfies: x^2 = A(x)^7 - A(x)^8 + x*A(x)^10.

Example

G.f. A(x) = 1 + x + 2*x^2 + 16*x^3 + 47*x^4 + 339*x^5 + 1166*x^6 + 8976*x^7 + 35651*x^8 + 278278*x^9 + 1212177*x^10 + 9302196*x^11 + 43167236*x^12 + 325489466*x^13 + 1589818896*x^14 + 11803540132*x^15 +...
such that A(x) = 1 + x*A(x)^3 - x^2/A(x)^7.
RELATED SERIES.
A(x)^3 = 1 + 3*x + 9*x^2 + 61*x^3 + 255*x^4 + 1551*x^5 + 7205*x^6 + 45045*x^7 + 228150*x^8 + 1461265*x^9 + 7819911*x^10 +...
1/A(x)^7 = 1 - 7*x + 14*x^2 - 84*x^3 + 385*x^4 - 1771*x^5 + 9394*x^6 - 50128*x^7 + 249088*x^8 - 1482285*x^9 + 7364203*x^10 +...
A(x)^7 = 1 + 7*x + 35*x^2 + 231*x^3 + 1330*x^4 + 8092*x^5 + 46956*x^6 + 284544*x^7 + 1684221*x^8 + 10313380*x^9 + 62148394*x^10 +...
A(x)^8 = 1 + 8*x + 44*x^2 + 296*x^3 + 1790*x^4 + 11112*x^5 + 66588*x^6 + 408824*x^7 + 2472261*x^8 + 15260520*x^9 + 93365184*x^10 +...
A(x)^10 = 1 + 10*x + 65*x^2 + 460*x^3 + 3020*x^4 + 19632*x^5 + 124280*x^6 + 788040*x^7 + 4947140*x^8 + 31216790*x^9 + 196150240*x^10 +...
where x^2 = A(x)^7 - A(x)^8 + x*A(x)^10.

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A = 1 + x*A^3 - x^2/A^7  +x*O(x^n)); polcoeff(G=A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Sequence in context: A254855 A181340 A275032 * A220173 A220801 A220250

Adjacent sequences: A295530 A295531 A295532 * A295534 A295535 A295536

Keyword

nonn

Author

Paul D. Hanna, Nov 23 2017

Status

approved