A189053 Expansion of d/dx log(1/(1-x/sqrt(1-4*x^2))).

1, 1, 7, 9, 41, 61, 225, 369, 1195, 2101, 6227, 11529, 32059, 61741, 163727, 325089, 831505, 1690981, 4206145, 8717049, 21215481, 44633821, 106782837, 227363409, 536618341, 1153594261, 2693492305, 5835080169, 13507578125, 29443836301

Offset

0,3

Links

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

Formula

G.f. sqrt(1-4*x^2)/(16*x^4+sqrt(1-4*x^2)*(4*x^3-x)-8*x^2+1),

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

Conjecture: n*a(n) +(n-1)*a(n-1) +(-13*n+12)*a(n-2) +(-13*n+25)*a(n-3) +4*(14*n-27) *a(n-4) +4*(14*n-41)*a(n-5) +80*(-n+3)*a(n-6) +80*(-n+4)*a(n-7)=0. - R. J. Mathar, Jun 14 2016

a(n) ~ 5^((n+1)/2). - Vaclav Kotesovec, Nov 17 2023

Prog

(Maxima) a(n):=n*sum((binomial((n-2)/2, (n-k)/2)*2^(n-k-1)*((-1)^(n-k)+1))/k, k, 1, n);
(PARI) x='x+O('x^66); /* that many terms */
Vec(deriv(log(1/(1-x/sqrt(1-4*x^2))))) /* show terms */ /* Joerg Arndt, Apr 16 2011 */

Crossrefs

Sequence in context: A032695 A323676 A007449 * A067649 A025631 A258183

Adjacent sequences: A189050 A189051 A189052 * A189054 A189055 A189056

Keyword

nonn

Author

Vladimir Kruchinin, Apr 16 2011

Status

approved