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 A036071 Expansion of 1/(1-5*x)^5. 7

%I

%S 1,25,375,4375,43750,393750,3281250,25781250,193359375,1396484375,

%T 9775390625,66650390625,444335937500,2905273437500,18676757812500,

%U 118286132812500,739288330078125,4566192626953125,27904510498046875

%N Expansion of 1/(1-5*x)^5.

%C With a different offset, number of n-permutations (n=5) of 6 objects u, v, w, z, x, y with repetition allowed, containing exactly four (4)u's. Example: a(1)=25 because we have uuuuv, uuuvu, uuvuu, uvuuu, vuuuu, uuuuw, uuuwu, uuwuu, uwuuu, wuuuu, uuuuz, uuuzu, uuzuu, uzuuu, zuuuu, uuuux, uuuxu, uuxuu, uxuuu, xuuuu uuuuy, uuuyu, uuyuu, uyuuu, yuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008

%F a(n) = binomial(n+4, 4)*5^n; G.f. 1/(1-5*x)^5.

%F a(0)=1, a(1)=25, a(2)=375, a(3)=4375, a(4)=43750, a(n)=25*a(n-1)- 250*a(n-2)+ 1250*a(n-3)-3125*a(n-4)+3125*a(n-5). - _Harvey P. Dale_, Mar 20 2013

%p seq(binomial(n+4,4)*5^n,n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008

%t CoefficientList[Series[1/(1-5x)^5,{x,0,30}],x] (* or *) LinearRecurrence[ {25,-250,1250,-3125,3125},{1,25,375,4375,43750},30] (* _Harvey P. Dale_, Mar 20 2013 *)

%o (Sage) [lucas_number2(n, 5, 0)*binomial(n,4)/5^4 for n in xrange(4, 23)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]

%Y A001787, A038846.

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_

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