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%I #8 May 25 2026 00:09:13
%S 1,20,35588,298222584,6893041104320,339390744700600960,
%T 30545941969311603920448,4541087129383087067300766208,
%U 1037530290355966843503848621711360,345178211314328731754914550691807848448,160358051712882281911114847531779916283438080,100600852780499610741720532655118892927017005940736
%N First column of the triangular array with T(0, m) = m^m and T(n, m) = T(n - 1, m + 3) - 2*T(n - 1, m + 2) + T(n - 1, m + 1).
%C This sequence is obtained by iterating the shift-difference operator E*(E - 1)^2 on f(m) = m^m and evaluating at m = 0, where E is the shift operator.
%F a(n) = Sum_{k=0..2*n} (-1)^k*binomial(2*n, k)*(n + k)^(n + k), with 0^0 = 1.
%e The triangular array begins:
%e m: 0 1 2 3 4 ...
%e --------------------------------------------------------------
%e n = 0 1 1 4 27 256 ...
%e n = 1 20 35588 298222584 ...
%e n = 2 35588 298222584 ...
%e n = 3 298222584 ...
%Y Cf. A000312, A395764, A069856.
%K nonn
%O 0,2
%A _Dalton Heilig_, May 18 2026