A190864 Expansion of 1/(1-x*sqrt(1+4*x^2)).

1, 1, 1, 3, 5, 5, 9, 21, 29, 31, 65, 143, 181, 183, 441, 1019, 1165, 893, 2929, 7829, 7589, 1677, 19305, 66585, 49661, -44279, 126881, 638085, 325525, -1024831, 833049, 6876389, 2135149, -16612625, 5467345, 81608271, 14007941, -244131809, 35877321

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Formula

a(n)=sum(k=1..n, binomial(k/2,(n-k)/2)*2^(n-k-1)*((-1)^(n-k)+1)), n>0, a(0)=1.

D-finite with recurrence: (-n+1)*a(n) +(-n+2)*a(n-1) +3*(-n+5)*a(n-2) +3*(-n+6)*a(n-3) +4*(2*n-5)*a(n-4) +4*(2*n-7)*a(n-5) +16*(n-4)*a(n-6) +16*(n-5)*a(n-7)=0. - R. J. Mathar, Jan 25 2020

Mathematica

CoefficientList[Series[1/(1-x Sqrt[1+4x^2]), {x, 0, 40}], x] (* Harvey P. Dale, Mar 04 2015 *)

Prog

(PARI) x='x+O('x^66); /* that many terms */
Vec(1/(1-x*sqrt(1+4*x^2))) /* show terms */ /* Joerg Arndt, May 22 2011 */
(Maxima) a(n):=sum(binomial(k/2, (n-k)/2)*2^(n-k-1)*((-1)^(n-k)+1), k, 1, n);

Crossrefs

Sequence in context: A120841 A145282 A049757 * A155537 A164663 A098971

Adjacent sequences: A190861 A190862 A190863 * A190865 A190866 A190867

Keyword

sign

Author

Vladimir Kruchinin, May 21 2011

Status

approved