The On-Line Encyclopedia of Integer Sequences (OEIS)

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A141344

Expansion of (2-sqrt(1+4x))/(2-x-sqrt(1+4x)).
(history; published version)

#10 by N. J. A. Sloane at Thu Jan 30 21:58:01 EST 2020

FORMULA

Conjectured to be D-finite conjecturewith recurrence: 3*(n-1)*a(n) +2*(2*n-11)*a(n-1) +(79-31*n)*a(n-2) +2*(2*n-5)*a(n-3)=0. - R. J. Mathar, Oct 25 2012

Discussion

Thu Jan 30

21:58

OEIS Server: https://oeis.org/edit/global/2848

#9 by R. J. Mathar at Fri Jan 24 16:28:16 EST 2020

STATUS

editing

approved

#8 by R. J. Mathar at Fri Jan 24 16:28:14 EST 2020

FORMULA

Apparently D-finite conjecture: 3*(n-1)*a(n) +2*(2*n-11)*a(n-1) +(79-31*n)*a(n-2) +2*(2*n-5)*a(n-3)=0. - R. J. Mathar, Oct 25 2012

STATUS

approved

editing

#7 by Harvey P. Dale at Mon Jan 14 11:32:16 EST 2013

STATUS

editing

approved

#6 by Harvey P. Dale at Mon Jan 14 11:32:13 EST 2013

MATHEMATICA

CoefficientList[Series[(2-Sqrt[1+4x])/(2-x-Sqrt[1+4x]), {x, 0, 30}], x] (* Harvey P. Dale, Jan 14 2013 *)

STATUS

approved

editing

#5 by R. J. Mathar at Thu Oct 25 15:05:05 EDT 2012

STATUS

editing

approved

#4 by R. J. Mathar at Thu Oct 25 14:18:00 EDT 2012

FORMULA

Apparently 3*(n-1)*a(n) +2*(2*n-11)*a(n-1) +(79-31*n)*a(n-2) +2*(2*n-5)*a(n-3)=0. - R. J. Mathar, Oct 25 2012

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:59:21 EDT 2012

COMMENTS

Image of A052961 under the Riordan array (c(-x),xc(-x)^2), c(x) the g.f. of A000108. [From _Paul Barry (pbarry(AT)wit.ie), _, Jan 29 2009]

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, Jun 26 2008

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/287

#2 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

COMMENTS

Image of A052961 under the Riordan array (c(-x),xc(-x)^2), c(x) the g.f. of A000108. [From Paul Barry (pbarry(AT)wit.ie), Jan 29 2009]

KEYWORD

easy,sign,new

#1 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

NAME

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

DATA

1, 1, 3, 7, 19, 45, 123, 285, 807, 1771, 5407, 10587, 37627, 57619, 279783, 231615, 2307339, -387531, 21769251, -28249347, 235837791, -539858235, 2857845723, -8509970007, 37342507167, -126289733319, 510715973643, -1837291760147

OFFSET

0,3

COMMENTS

Row sums of A141343. Hankel transform is 2^n.

KEYWORD

easy,sign,new

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Jun 26 2008

STATUS

approved