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%I #47 Mar 16 2023 04:54:19
%S 0,1,4,30,320,4400,73872,1462552,33325056,858283776,24641000000,
%T 779935205984,26972930949120,1011642325897216,40890444454377728,
%U 1771640957790000000,81896889467638120448,4022826671022707900416,209224123984489179202560
%N a(0) = 0; a(n) = ( (n + sqrt(n))^n - (n - sqrt(n))^n )/(2 * sqrt(n)).
%F a(n) = Sum_{k=0..floor((n-1)/2)} n^(n-1-k) * binomial(n,2*k+1).
%F a(n) = [x^n] x/(1 - 2*n*x + (n-1)*n*x^2).
%F a(n) = n! * [x^n] exp(n * x) * sinh(sqrt(n) * x) / sqrt(n) for n > 0.
%o (PARI) a(n) = polcoeff(lift(Mod('x, ('x-n)^2-n)^n), 1); \\ _Kevin Ryde_, Mar 16 2023
%Y Main diagonal of A361290.
%Y Cf. A007070, A030192, A093145, A154237.
%Y Cf. A084062.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Mar 11 2023
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