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A099324 Expansion of (1 + sqrt(1 + 4x))/(2(1 + x)). 3
1, 0, -1, 3, -8, 22, -64, 196, -625, 2055, -6917, 23713, -82499, 290511, -1033411, 3707851, -13402696, 48760366, -178405156, 656043856, -2423307046, 8987427466, -33453694486, 124936258126, -467995871776, 1757900019100, -6619846420552, 24987199492704, -94520750408708 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Binomial transform is A099323. Second binomial transform is A072100.

Hankel transform is A049347. - Paul Barry, Aug 10 2009

LINKS

Robert Israel, Table of n, a(n) for n = 0..1668

FORMULA

a(n) = Sum_{k=0..2n} (2*0^(2n-k)-1)*C(k,floor(k/2)). - Paul Barry, Aug 10 2009

|a(n+2)| = A091491(n+2,2). - Philippe Deléham, Nov 25 2009

G.f.: T(0)/(2+2*x)), where T(k) = k+2 - 2*x*(2*k+1) + 2*x*(k+2)*(2*k+3)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 27 2013

(2+4*n)*a(n) + (4+5*n)*a(n+1) + (n+2)*a(n+2) = 0. - Robert Israel, Mar 27 2018

MAPLE

f:= gfun:-rectoproc({(2+4*n)*a(n)+(4+5*n)*a(n+1)+(n+2)*a(n+2), a(0) = 1, a(1) = 0}, a(n), remember):

map(f, [$0..50]); # Robert Israel, Mar 27 2018

MATHEMATICA

CoefficientList[Series[(1+Sqrt[1+4x])/(2(1+x)), {x, 0, 40}], x] (* Harvey P. Dale, Jan 30 2014 *)

CROSSREFS

Cf. A014138.

Sequence in context: A047926 A192681 A014138 * A290898 A117420 A003101

Adjacent sequences:  A099321 A099322 A099323 * A099325 A099326 A099327

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 12 2004

STATUS

approved

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Last modified August 19 15:49 EDT 2018. Contains 313877 sequences. (Running on oeis4.)