A144578 Denominators of expansion of exp(1-sqrt(1-x-2*x^2)).

1, 2, 4, 48, 384, 1920, 46080, 129024, 1032192, 185794560, 3715891200, 40874803200, 78479622144, 10202350878720, 64924051046400, 42849873690624000, 1371195958099968000, 4662066257539891200, 335668770542872166400, 5797915127558701056000

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..404

Formula

A144577/A144578 is D-finite with recurrence 64*b(n) + 48*b(n+1) + (32*n^2 + 96*n + 76)*b(n+2) + (24*n^2 + 120*n + 145)*b(n+3) + (-12*n^2 - 66*n - 72)*b(n+4) + (-4*n^2 - 36*n - 80)*b(n+5)=0. - Robert Israel, Dec 17 2020

Example

1 + (1/2)*x + (5/4)*x^2 + (55/48)*x^3 + (757/384)*x^4 + (4973/1920)*x^5 + (...

Maple

f:= gfun:-rectoproc({64*a(n) + 48*a(n + 1) + (32*n^2 + 96*n + 76)*a(n + 2) + (24*n^2 + 120*n + 145)*a(n + 3) + (-12*n^2 - 66*n - 72)*a(n + 4) + (-4*n^2 - 36*n - 80)*a(n + 5), a(0) = 1, a(1) = 1/2, a(2) = 5/4, a(3) = 55/48, a(4) = 757/384}, a(n), remember):
map(denom@f, [$0..30]); # Robert Israel, Dec 17 2020

Mathematica

CoefficientList[Series[Exp[1-Sqrt[1-x-2x^2]], {x, 0, 20}], x]//Denominator (* Harvey P. Dale, Jul 12 2023 *)

Crossrefs

Cf. A144577.

Sequence in context: A298903 A127211 A144580 * A143968 A308665 A097424

Adjacent sequences: A144575 A144576 A144577 * A144579 A144580 A144581

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 07 2009

Status

approved