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%I #6 Oct 09 2017 09:05:52
%S 1,6,-84,4704,-345744,34689648,-4214388864,601692751296,
%T -98355859080192,18095231814398592,-3699821591569942272,
%U 832503662673228725760,-204513977951411795896320,54487882834444658521294848,-15654578707586867016637562880,4826050889976725020111217528832
%N G.f.: A(x) satisfies: A( 8*x - 7*A(x) ) = x - 36*x^2.
%H Vaclav Kotesovec, <a href="/A293455/b293455.txt">Table of n, a(n) for n = 1..296</a>
%F a(n) ~ (-1)^n * c * (42/log(7))^n * n! / n^(5/7 + 2*log(7)/3), where c = 0.0333062243645475214012...
%o (PARI) {a(n) = my(A=x, V=[1, 6]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(A, x, 8*x - 7*A) )[#V]/6 ); V[n]}
%o for(n=1, 30, print1(a(n), ", "))
%Y Cf. A291198, A292812, A292813, A292814, A293454, A293456.
%K sign
%O 1,2
%A _Vaclav Kotesovec_, Oct 09 2017