A293456 G.f.: A(x) satisfies: A( 9*x - 8*A(x) ) = x - 49*x^2.

1, 7, -112, 7616, -659456, 79478784, -11601838080, 1999116435456, -395724994904064, 88421930838786048, -22013644829198647296, 6044770041860462739456, -1815656770444555192369152, 592444471359892990392795136, -208760047583926706433769340928

Offset

1,2

Comments

Conjecture: In general, if k > 0 and g.f. A(x) satisfies A((k+2)*x - (k+1)*A(x)) = x - (k*x)^2, then a(n) ~ (-1)^n * c(k) * (k*(k+1)/log(k+1))^n * n! / n^((k-1)/(k+1) + (k-2)*log(k+1)/k), where c(k) is a constant.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..288

Formula

a(n) ~ (-1)^n * c * (56/log(8))^n * n! / n^(3/4 + 15*log(2)/7), where c = 0.0288378187676139223379...

Prog

(PARI) {a(n) = my(A=x, V=[1, 7]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(A, x, 9*x - 8*A) )[#V]/7 ); V[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A291198, A292812, A292813, A292814, A293454, A293455.

Sequence in context: A359927 A010795 A377639 * A099153 A270121 A079296

Adjacent sequences: A293453 A293454 A293455 * A293457 A293458 A293459

Keyword

sign

Author

Vaclav Kotesovec, Oct 09 2017

Status

approved