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
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).
Programs
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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 *) -
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
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