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%I #7 Aug 30 2023 03:16:45
%S 1,1,2,7,24,86,313,1157,4325,16303,61856,235917,903620,3473381,
%T 13391280,51761781,200523644,778342906,3026400508,11785538461,
%U 45959004812,179444813270,701422450293,2744562302533,10749124666643,42135320616531
%N Main diagonal of A139755, the table of q-derangement numbers of type A.
%H Vaclav Kotesovec, <a href="/A141753/b141753.txt">Table of n, a(n) for n = 1..230</a>
%F a(n) = [q^n] { ([n+1]_q)! * Sum_{m=0..n+1} (-1)^m * q^(m(m-1)/2) / ([m]_q)! }; here, the q-factorial of n is denoted by ([n]_q)! = Product_{j=1..n} (1-q^j)/(1-q).
%F a(n) ~ c * 4^n / sqrt(Pi*n), where c = A048651^2 = QPochhammer(1/2)^2 = 0.083398563863748521534541808155312... - _Vaclav Kotesovec_, Aug 30 2023
%o (PARI) {a(n)=polcoeff(prod(j=1,n+1,(1-q^j)/(1-q))* sum(k=0,n+1,(-1)^k*q^(k*(k-1)/2)/if(k==0,1,prod(j=1,k,(1-q^j)/(1-q)))),n,q)}
%Y Cf. A139755, A141754.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jul 05 2008
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