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A318593 Number of n-member subsets of [5*n] whose elements sum to a multiple of five.

%I A318593 #17 Mar 27 2019 03:57:10
%S A318593 1,1,9,91,969,10630,118755,1344904,15380937,177232627,2054455670,
%T A318593 23930713170,279871768995,3284214703056,38650751381832,
%U A318593 456002537343580,5391644226101705,63871405575418665,757929628541719755,9007607943130625829,107196674080761940470
%N A318593 Number of n-member subsets of [5*n] whose elements sum to a multiple of five.
%H A318593 Alois P. Heinz, <a href="/A318593/b318593.txt">Table of n, a(n) for n = 0..922</a>
%F A318593 a(n) = floor(A163456(n)) + [n mod 5 = 0]*A163455(n/5), with A163456(n) = binomial(5*n,n)/5 and A163455(n) = binomial(5*n-1,n) where [] is an Iverson bracket. - _Georg Fischer_, Mar 23 2019
%e A318593 a(2) = 9: {1,4}, {1,9}, {2,3}, {2,8}, {3,7}, {4,6}, {5,10}, {6,9}, {7,8}.
%p A318593 b:= proc(n, s, m, t) option remember; `if`(n=0, `if`(s=0 and t=0, 1, 0),
%p A318593       b(n-1, s, m, t)+`if`(t=0, 0, b(n-1, irem(s+n, m), m, t-1)))
%p A318593     end:
%p A318593 a:= n-> b(5*n, 0, 5, n):
%p A318593 seq(a(n), n=0..27);
%Y A318593 Column k=5 of A318557.
%Y A318593 Cf. A163455, A163456.
%K A318593 nonn
%O A318593 0,3
%A A318593 _Alois P. Heinz_, Aug 29 2018