A028258 Expansion of 1/((1-2*x)*(1-4*x)(1-8*x)(1-16*x)).

1, 30, 620, 11160, 188976, 3108960, 50434240, 812507520, 13044728576, 209073047040, 3348029967360, 53591377582080, 857645259698176, 13723790036459520, 219592368170516480, 3513571713573027840, 56217898008516427776, 899492372901406310400

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (30,-280,960,-1024).

Formula

Difference of Gaussian binomial coefficients [ n+1, 4 ]-[ n, 4 ] (n >= 3).

a(n) = 30*a(n-1)-280*a(n-2)+960*a(n-3)-1024*a(n-4), with a(0)=1, a(1)=30, a(2)=620, a(3)=11160. - Harvey P. Dale, Jun 18 2011

a(n) = (2^n*(2^(n+1)-1)*(2^((n+1)+1)-1)*(2^(n+3)-1))/21. - Harvey P. Dale, Jun 18 2011; offset corrected by Charles R Greathouse IV, Feb 10 2017

E.g.f.: exp(2*x)*(64*exp(14*x) - 56*exp(6*x) + 14*exp(2*x) - 1)/21. - Stefano Spezia, Jun 23 2022

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-8x)(1-16x)), {x, 0, 50}], x] (* or *) LinearRecurrence[{30, -280, 960, -1024}, {1, 30, 620, 11160}, 50] (* or *) Table[(2^(n-1)(2^n-1)(2^(n+1)-1)(2^(n+2)-1))/21, {n, 20}] (* Harvey P. Dale, Jun 18 2011 *)

Prog

(PARI) a(n)=(2^n*(2^(n+1)-1)*(2^((n+1)+1)-1)*(2^(n+3)-1))/21 \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A006516, A016290, A006097.

Sequence in context: A277877 A279870 A124099 * A285235 A075911 A001719

Adjacent sequences: A028255 A028256 A028257 * A028259 A028260 A028261

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved