A144579 Numerators of expansion of exp(1-sqrt(1-x-x^2)).

1, 1, 3, 31, 301, 571, 51751, 926731, 3281851, 479961901, 13256384851, 9729091003, 13915350562081, 74105896232383, 3502203417248521, 919071064063596151, 43167975952565245501, 361179801176946547051, 16542165057245024351233, 6561750899663711363984851

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..377

Formula

Expansion satisfies 8*a(n)+12*a(n+1)+(22+8*n^2+24*n)*a(n+2)+(73+12*n^2+60*n)*a(n+3)+(-18*n-8-4*n^2)*a(n+4)+(-4*n^2-36*n-80)*a(n+5)=0. - Robert Israel, Dec 31 2019

Example

The expansion is 1 + (1/2)*x + (3/4)*x^2 + (31/48)*x^3 + (301/384)*x^4 + (571/640)*x^5 + (51751/46080)*x^6 + ( 926731/645120)*x^7 + (3281851/1720320)*x^8 + ...

Maple

g:= gfun:-rectoproc({8*a(n)+12*a(n+1)+(22+8*n^2+24*n)*a(n+2)+(73+12*n^2+60*n)*a(n+3)+(-18*n-8-4*n^2)*a(n+4)+(-4*n^2-36*n-80)*a(n+5), a(0) = 1, a(1) = 1/2, a(2) = 3/4, a(3) = 31/48, a(4) = 301/384}, a(n), remember):
seq(numer(g(n)), n=0..40); # Robert Israel, Dec 31 2019

Mathematica

CoefficientList[Series[Exp[1-Sqrt[1-x-x^2]], {x, 0, 20}], x]//Numerator (* Harvey P. Dale, Dec 26 2018 *)

Crossrefs

Cf. A144580.

Sequence in context: A212730 A236957 A112425 * A348709 A220997 A222094

Adjacent sequences: A144576 A144577 A144578 * A144580 A144581 A144582

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 07 2009

Status

approved