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A126967 Expansion of e.g.f.: sqrt(1+4*x)/(1+2*x). 4
1, 0, -4, 48, -624, 9600, -175680, 3790080, -95235840, 2752081920, -90328089600, 3328103116800, -136191650918400, 6131573025177600, -301213549769932800, 16030999766605824000, -918678402394841088000, 56387623092958789632000, -3690023220507773140992000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A row of an array that is under investigation.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..365

FORMULA

D-finite with recurrence: a(n) +6*(n-1)*a(n-1) +4*(n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jan 23 2020

MAPLE

seq(coeff(series( sqrt(1+4*x)/(1+2*x), x, n+1)*n!, x, n), n = 0..20); # G. C. Greubel, Jan 29 2020

MATHEMATICA

nmax=20; CoefficientList[Series[Sqrt[1 + 4 x] / (1 + 2 x), {x, 0, nmax}], x] Range[0, nmax]! (* Vincenzo Librandi, Jan 24 2020 *)

PROG

(MAGMA) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Sqrt(1+4*x)/(1+2*x))); [Factorial(n-1)*b[n]: n in [1..m]]; // Vincenzo Librandi, Jan 24 2020

(PARI) my(x='x+O('x^30)); Vec(serlaplace( sqrt(1+4*x)/(1+2*x) )) \\ G. C. Greubel, Jan 29 2020

(Sage) [factorial(n)*( sqrt(1+4*x)/(1+2*x) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Jan 29 2020

CROSSREFS

Cf. A126966.

Sequence in context: A220325 A265419 A226705 * A098402 A333481 A003774

Adjacent sequences:  A126964 A126965 A126966 * A126968 A126969 A126970

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Mar 22 2007

STATUS

approved

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)