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a(n) = (1/n!) * Sum_{i_1=1..n} Sum_{i_2=1..n} ... Sum_{i_n=1..n} multinomial(i_1+i_2+...+i_n; i_1, i_2, ... , i_n).
4

%I #25 May 24 2019 12:39:03

%S 1,1,7,842,7958726,15467641899285,10893033763705794846727,

%T 4247805448772073978048752721163278,

%U 1299618941291522676629215597535104557826094801396,419715170056359079715862408734598208208707081189266290220651371206

%N a(n) = (1/n!) * Sum_{i_1=1..n} Sum_{i_2=1..n} ... Sum_{i_n=1..n} multinomial(i_1+i_2+...+i_n; i_1, i_2, ... , i_n).

%H Seiichi Manyama, <a href="/A308296/b308296.txt">Table of n, a(n) for n = 0..27</a>

%F a(n) = A144510(n,n).

%e a(2) = (1/2) * (binomial(1+1,1) + binomial(1+2,2) + binomial(2+1,1) + binomial(2+2,2)) = 7.

%o (PARI) {a(n) = sum(i=n, n^2, i!*polcoef(sum(j=1, n, x^j/j!)^n, i))/n!}

%Y Cf. A144510, A144512, A274762, A281901.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 19 2019