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%I #11 Sep 09 2019 01:41:55
%S 0,0,0,0,0,5,6,14,24,45,70,110,156,234,322,450,592,799,1026,1330,1680,
%T 2121,2618,3243,3936,4800,5746,6885,8148,9657,11310,13237,15360,17820,
%U 20502,23590,26928,30747,34884,39546,44600,50266,56364,63167,70488,78615
%N Sum of all the parts in the partitions of n into 5 parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = n * A026811(n).
%F a(n) = A308823(n) + A308824(n) + A308825(n) + A308826(n) + A308827(n).
%e The partitions of n into 5 parts for n = 10, 11, ..
%e 1+1+1+1+10
%e 1+1+1+2+9
%e 1+1+1+3+8
%e 1+1+1+4+7
%e 1+1+1+5+6
%e 1+1+1+1+9 1+1+2+2+8
%e 1+1+1+2+8 1+1+2+3+7
%e 1+1+1+3+7 1+1+2+4+6
%e 1+1+1+4+6 1+1+2+5+5
%e 1+1+1+5+5 1+1+3+3+6
%e 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e 1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4
%e 1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4
%e 1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6
%e 1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5
%e 1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4
%e 1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4
%e 2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3
%e --------------------------------------------------------------------------
%e n | 10 11 12 13 14 ...
%e --------------------------------------------------------------------------
%e a(n) | 70 110 156 234 322 ...
%e --------------------------------------------------------------------------
%e - _Wesley Ivan Hurt_, Sep 08 2019
%t Table[n*Sum[Sum[Sum[Sum[1, {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 100}]
%Y Cf. A026811, A308823, A308824, A308825, A308826, A308827.
%K nonn
%O 0,6
%A _Wesley Ivan Hurt_, Jun 26 2019