A171992 G.f. satisfies: A(x) = x + A(A(x))^2 - A(A(x))^4.

1, 1, 4, 23, 166, 1380, 12684, 125857, 1328084, 14754242, 171338020, 2069009164, 25877555908, 334197713580, 4445788022944, 60800921601639, 853479846713406, 12280659254071964, 180929894848439516, 2726751302240331150, 42001984460083899448, 660800371941797598828

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Formula

G.f. satisfies: A( x - A(x)^2 + A(x)^4 ) = x.

Example

G.f.: A(x) = x + x^2 + 4*x^3 + 23*x^4 + 166*x^5 + 1380*x^6 + 12684*x^7 +...
Related series begin:
A(A(x)) = x + 2*x^2 + 10*x^3 + 67*x^4 + 538*x^5 + 4866*x^6 + 48000*x^7 +...
A(A(x))^2 = x^2 + 4*x^3 + 24*x^4 + 174*x^5 + 1444*x^6 + 13224*x^7 +...
A(A(x))^4 = x^4 + 8*x^5 + 64*x^6 + 540*x^7 + 4856*x^8 + 46352*x^9 +...
A(x)^2 = x^2 + 2*x^3 + 9*x^4 + 54*x^5 + 394*x^6 + 3276*x^7 + 29985*x^8 +...
A(x)^4 = x^4 + 4*x^5 + 22*x^6 + 144*x^7 + 1085*x^8 + 9100*x^9 +...
where the series reversion of the g.f. A(x) begins:
x - A(x)^2 + A(x)^4 = x - x^2 - 2*x^3 - 8*x^4 - 50*x^5 - 372*x^6 - 3132*x^7 -...

Prog

(PARI) {a(n)=local(A=x+x^2, B=x); for(i=1, n, B=subst(A, x, A+x*O(x^n)); A=x+B^2-B^4); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=serreverse(x-A^2+A^4+x*O(x^n))); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A190761, A171991, A213591.

Sequence in context: A307402 A354497 A111547 * A158884 A317057 A053525

Adjacent sequences: A171989 A171990 A171991 * A171993 A171994 A171995

Keyword

nonn

Author

Paul D. Hanna, Jun 27 2012

Status

approved