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Number of compositions (ordered partitions) of n into distinct parts, the least being 6.
3

%I #5 Nov 26 2020 09:16:38

%S 0,0,0,0,0,0,1,0,0,0,0,0,0,2,2,2,2,2,2,2,2,8,8,14,14,20,20,26,26,32,

%T 56,62,86,116,140,170,218,248,296,350,518,572,764,938,1250,1448,1880,

%U 2198,2774,3212,3908,5210,6146,7568,9368,11750,14510,17756,21476,26402,31826,38432,45536

%N Number of compositions (ordered partitions) of n into distinct parts, the least being 6.

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: Sum_{k>=1} k! * x^(k*(k + 11)/2) / Product_{j=1..k-1} (1 - x^j).

%e a(21) = 8 because we have [15, 6], [8, 7, 6], [8, 6, 7], [7, 8, 6], [7, 6, 8], [6, 15], [6, 8, 7] and [6, 7, 8].

%t nmax = 62; CoefficientList[Series[Sum[k! x^(k (k + 11)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A026799, A026827, A339104, A339162, A339163, A339164, A339165, A339166, A339170, A339171, A339172.

%K nonn

%O 0,14

%A _Ilya Gutkovskiy_, Nov 25 2020