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%I #15 Sep 08 2022 08:45:57
%S 1,256,9842,131072,976563,5038848,20176804,67108864,193710245,
%T 500000000,1178973846,2579890176,5302249687,10330523392,19221679688,
%U 34359738368,59293938249,99179645184,161343848890,256000000000,397140023291,603634608896,900576330732,1320903770112,1907348632813,2714751839488
%N Number of compositions of even numbers into 9 parts <= n.
%C Number of ways of placing an even number of indistinguishable objects in 9 distinguishable boxes with the condition that each box can hold most n objects.
%H Vincenzo Librandi, <a href="/A191496/b191496.txt">Table of n, a(n) for n = 0..1000</a>
%H Adi Dani, <a href="https://oeis.org/wiki/User:Adi_Dani_/Restricted_compositions_of_natural_numbers">Restricted compositions of natural numbers</a>
%F a(n)= ( (n+1)^9 + (1 + (-1)^n)/2 )/2.
%F a(n) = 9*a(n-1) - 35*a(n-2) + 75*a(n-3) - 90*a(n-4) + 42*a(n-5) + 42*a(n-6) - 90*a(n-7) + 75*a(n-8) - 35*a(n-9) + 9*a(n-10) - a(n-11).
%F G.f.: (1 + 247*x + 7573*x^2 + 51379*x^3 + 122275*x^4 + 122149*x^5 + 51463*x^6 + 7537*x^7 + 256*x^8) / ( (1+x)*(1-x)^10 ). - _R. J. Mathar_, Jun 06 2011
%e a(1)=256: there are 256 compositions of even numbers into 9 parts <= 1:
%e 0: (0,0,0,0,0,0,0,0,0) --> 9!/9!0! = 1
%e 2: (0,0,0,0,0,0,0,1,1) --> 9!/7!2! = 36
%e 4: (0,0,0,0,0,1,1,1,1) --> 9!/5!4! = 126
%e 8: (0,0,0,1,1,1,1,1,1) --> 9!/3!6! = 84
%e 10: (0,1,1,1,1,1,1,1,1) --> 9!/1!8! = 9
%t Table[1/2*((n + 1)^9 + (1 + (-1)^n)*1/2), {n, 0, 25}]
%o (Magma) [( (n+1)^9 + (1+(-1)^n)/2 )/2: n in [0..30]]; // _Vincenzo Librandi_, Jun 16 2011
%K nonn
%O 0,2
%A _Adi Dani_, Jun 03 2011
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