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%I #42 Jan 21 2022 08:17:24
%S 1,1,10,450,55456,14480700,6878394720,5373548250000,6427291156586496,
%T 11157501095973529920,26968983444160450560000,
%U 87808164603589940623344000,374818412822626584819196231680,2050842983500342507649178541536000,14112022767608502582976078751055052800
%N Permanent of the n X n matrix with numbers 1,2,...,n^2 in order across rows.
%H Max Alekseyev, <a href="/A232773/b232773.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = (-1)^n * Sum_{k=0..n} n^k * Stirling1(n,n-k) * Stirling1(n+1,k+1) * (n-k)! * k!. - _Max Alekseyev_, Nov 30 2013
%F Limit n->infinity a(n)^(1/n)/n^3 = exp(-2). - _Vaclav Kotesovec_, Nov 30 2013
%F a(n) = A232788(n)*n!!, where n!! = A006882(n) is the double-factorial. - _M. F. Hasler_, Nov 30 2013
%p a:= n-> (-1)^n*add(n^k*Stirling1(n, n-k)*
%p Stirling1(n+1, k+1)*(n-k)!*k!, k=0..n):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Dec 02 2013
%t Table[(-1)^n * Sum[n^k * StirlingS1[n, n-k] * StirlingS1[n+1, k+1] * (n-k)! * k!,{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_ after _Max Alekseyev_, Nov 30 2013 *)
%o (PARI) a(n) = (-1)^n * sum(k=0,n, n^k * stirling(n,n-k) * stirling(n+1,k+1) * (n-k)! * k! ) /* _Max Alekseyev_, Nov 30 2013 */
%Y Cf. A114533, A232788, A008277, A232818, A204248, A094638.
%K nonn
%O 0,3
%A _Franklin T. Adams-Watters_, Nov 30 2013
%E More terms from _W. Edwin Clark_, Nov 30 2013
%E a(0)=1 prepended by _Alois P. Heinz_, Dec 02 2013
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