A185966 Series reversion of A028310.

1, -1, 0, 2, -2, -5, 14, 5, -72, 68, 278, -726, -520, 4691, -3514, -21758, 50374, 56185, -374566, 194596, 1962618, -3956504, -6258320, 33057877, -8974630, -190822072, 330170022, 710487590, -3088268200, 18008739, 19398384974, -28292606291, -81631282280, 298546543220, 84094857302, -2028216574806, 2428288153424, 9450205225145

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = A185962(2*n,n)/(n+1) = A185965(n)/(n+1).

Given g.f. A(x) then B(x) = x * A(x) satisfies B(x) = (1 - B(x)) * (x + B(x) * (B(x) - x)). - Michael Somos, Apr 05 2012

Conjecture: 6*n*(n+1)*a(n) -n*(n-14)*a(n-1) +2*n*(14*n-19)*a(n-2) -4*(n-2)*(17*n-48)*a(n-3) +6*(2*n-5)*(n-4)*a(n-4)=0. - R. J. Mathar, Nov 15 2012

Recurrence (of order 3): 3*n*(n+1)*(19*n-27)*a(n) = -2*n*(38*n^2 - 73*n + 9)*a(n-1) - 20*(19*n^3 - 65*n^2 + 66*n - 18)*a(n-2) + 2*(n-3)*(2*n-3)*(19*n-8)*a(n-3). - Vaclav Kotesovec, Jan 22 2014

Lim sup n->infinity |a(n)|^(1/n) = sqrt(20/9 + 1/27*(272376 - 12312 * sqrt(57))^(1/3) + 2/9*(1261 + 57 * sqrt(57))^(1/3)) = 2.637962913244886521522... - Vaclav Kotesovec, Jan 22 2014

Example

1 - x + 2*x^3 - 2*x^4 - 5*x^5 + 14*x^6 + 5*x^7 - 72*x^8 + 68*x^9 + ...

Mathematica

CoefficientList[1/x*InverseSeries[Series[x*(1-x+x^2) /(1-x)^2, {x, 0, 20}], x], x] (* Vaclav Kotesovec, Jan 22 2014 *)

Prog

(PARI) {a(n) = if( n<0, 0, polcoeff( serreverse( x * ((1 - x + x^2) / (1 - x)^2 + x * O(x^n))) / x, n))} /* Michael Somos, Apr 05 2012 */
(PARI) {a(n) = local(B); if( n<0, 0, B = O(x); for( k=0, n, B = (1 - B) * (x + B * (B - x))); polcoeff( B / x, n))} /* Michael Somos, Apr 05 2012 */

Crossrefs

Cf. A028130, A185962, A185965.

Sequence in context: A208392 A282275 A208201 * A032097 A176856 A112709

Adjacent sequences: A185963 A185964 A185965 * A185967 A185968 A185969

Keyword

sign,easy

Author

Paul Barry, Feb 07 2011

Status

approved