A292813 G.f.: A(x) satisfies: A( 5*x - 4*A(x) ) = x - 9*x^2.

1, 3, -24, 624, -23040, 1102848, -63320064, 4204118016, -315301920768, 26294301622272, -2410825799172096, 240940701368451072, -26069519382431662080, 3036630253199488450560, -378975438359301231476736, 50464427995254851962404864, -7143619061783407156694876160, 1071471673355571318056420376576, -169778310385940944720470768353280, 28343313796900390128748827210940416, -4972974647067348293267827631390195712

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n) for n = 1..200

Formula

a(n) ~ (-1)^n * c * 6^n * n! / (n^(1/2 + 2*log(2)/3) * (log(2))^n), where c = 0.04600302526929... - Vaclav Kotesovec, Oct 09 2017

Example

G.f.: A(x) = x + 3*x^2 - 24*x^3 + 624*x^4 - 23040*x^5 + 1102848*x^6 - 63320064*x^7 + 4204118016*x^8 - 315301920768*x^9 + 26294301622272*x^10 - 2410825799172096*x^11 + 240940701368451072*x^12 - 26069519382431662080*x^13 + 3036630253199488450560*x^14 - 378975438359301231476736*x^15 +...
such that A( 5*x - 4*A(x) ) = x - 9*x^2.
RELATED SERIES.
Define Ai(x) such that Ai(A(x)) = x, then Ai(x) begins:
Ai(x) = x - 3*x^2 + 42*x^3 - 1119*x^4 + 41670*x^5 - 1961790*x^6 + 110327892*x^7 - 7171123959*x^8 + 527249131182*x^9 - 43195371425274*x^10 +...
where Ai(x - 9*x^2) = 5*x - 4*A(x).

Prog

(PARI) {a(n) = my(A=x, V=[1, 3]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(A, x, 5*x - 4*A) )[#V]/3 ); V[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A291198, A292812, A292814, A292811, A293454, A293455, A293456.

Sequence in context: A330297 A109055 A318766 * A293249 A202944 A056207

Adjacent sequences: A292810 A292811 A292812 * A292814 A292815 A292816

Keyword

sign

Author

Paul D. Hanna, Sep 23 2017

Status

approved