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a(n) = [x^n] Product_{k=0..2*n-1} (x + (-1)^k * k).
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%I #13 Sep 26 2021 02:27:09

%S 1,-1,-5,51,1009,-17765,-636385,15875083,828730833,-26734633497,

%T -1837389309405,72689703927555,6202163408816881,-290609121018808813,

%U -29631450442239587305,1604436906627413556075,190333687041180914380065,-11692931012450127257939505,-1582217617564533519968758645

%N a(n) = [x^n] Product_{k=0..2*n-1} (x + (-1)^k * k).

%H Seiichi Manyama, <a href="/A348023/b348023.txt">Table of n, a(n) for n = 0..351</a>

%F a(n) = A047991(2*n-1,n) for n>0.

%o (PARI) a(n) = polcoef(prod(k=0, 2*n-1, x+(-1)^k*k), n);

%Y Cf. A047991, A187646, A348024.

%K sign

%O 0,3

%A _Seiichi Manyama_, Sep 25 2021