A292812 G.f.: A(x) satisfies: A( 4*x - 3*A(x) ) = x - 4*x^2.

1, 2, -12, 216, -5616, 186624, -7387200, 335736576, -17124804864, 965515500288, -59526188983296, 3980690988235776, -286917239797788672, 22174720816561975296, -1829668999418480590848, 160570117472696852299776, -14937971163165634577301504, 1468791751381133837013319680, -152229793395391092702181785600, 16589818156062623434747885780992, -1896733533500219982388526312325120

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..330 (terms 1..200 from Paul D. Hanna)

Formula

a(n) ~ (-1)^n * c * 6^n * n! / (n^(1/3) * (log(3))^n), where c = 0.04217549814791850977595... - Vaclav Kotesovec, Oct 09 2017

Example

G.f.: A(x) = x + 2*x^2 - 12*x^3 + 216*x^4 - 5616*x^5 + 186624*x^6 - 7387200*x^7 + 335736576*x^8 - 17124804864*x^9 + 965515500288*x^10 - 59526188983296*x^11 + 3980690988235776*x^12 - 286917239797788672*x^13 + 22174720816561975296*x^14 - 1829668999418480590848*x^15 +...
such that A( 4*x - 3*A(x) ) = x - 4*x^2.
RELATED SERIES.
Define Ai(x) such that Ai(A(x)) = x, then Ai(x) begins:
Ai(x) = x - 2*x^2 + 20*x^3 - 376*x^4 + 9872*x^5 - 325056*x^6 + 12684480*x^7 - 567616512*x^8 + 28519993088*x^9 - 1585862993152*x^10 + 96566543541248*x^11 +...
where Ai(x - 4*x^2) = 4*x - 3*A(x).

Prog

(PARI) {a(n) = my(A=x, V=[1, 2]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(A, x, 4*x - 3*A) )[#V]/2 ); V[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A291198, A292813, A292814, A292811, A293454, A293455, A293456.

Sequence in context: A129893 A008352 A082491 * A153302 A123118 A367051

Adjacent sequences: A292809 A292810 A292811 * A292813 A292814 A292815

Keyword

sign

Author

Paul D. Hanna, Sep 23 2017

Status

approved