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%I #17 Apr 16 2023 10:42:35
%S 0,64,1093,8192,39062,139968,411771,1048576,2391484,5000000,9743585,
%T 17915904,31374258,52706752,85429687,134217728,205169336,306110016,
%U 446935869,640000000,900544270,1247178944,1702412723,2293235712,3051757812,4015905088
%N Number of compositions of odd natural numbers into 7 parts <=n
%H Adi Dani, <a href="https://oeis.org/wiki/User:Adi_Dani_/Restricted_compositions_of_natural_numbers">Restricted compositions of natural numbers</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (7,-20,28,-14,-14,28,-20,7,-1).
%F a(n) = ((n + 1)^7 - (1 + (-1)^n)/2)/2.
%F a(2*n+1) = A191494(2*n+1); a(2*n) = A191494(2*n)-1.
%F G.f.: x*(64+645*x+1821*x^2+1786*x^3+666*x^4+57*x^5+x^6) / ( (1+x)*(x-1)^8 ). - _R. J. Mathar_, Jun 22 2011
%e a(1)=64: the 64 compositions of odd numbers into 7 parts <=1
%e 1:(0,0,0,0,0,0,1)-->7!/(6!1!)= 7
%e 3:(0,0,0,0,1,1,1)-->7!/(4!3!)=35
%e 5:(0,0,1,1,1,1,1)-->7!/(2!5!)=21
%e 7:(1,1,1,1,1,1,1)-->7!/(0!7!)= 1.
%t Table[Floor[1/2*((n + 1)^7 - (1 + (-1)^n)/2)], {n, 0, 25}]
%o (PARI) a(n)=((n+1)^7-(1+(-1)^n)/2)/2 \\ _Charles R Greathouse IV_, Jul 06 2017
%K nonn,easy
%O 0,2
%A _Adi Dani_, Jun 19 2011
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