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%I #8 May 24 2026 23:59:35
%S 1,23,40662,339512814,7833320861072,385274862872862320,
%T 34651074659044387342080,5148782075953899427664208008,
%U 1175932058880268594539875051459264,391109408932914016441213394462369295744,181653878605153955962729835740045223980699520,113939186843560221433330434261292079705499930804224
%N First column of the triangular array with T(0, m) = m^m and T(n, m) = T(n - 1, m + 3) - T(n - 1, m + 2).
%C This sequence is obtained by iterating the shift-difference operator E^2*(E - 1) on f(m) = m^m and evaluating at m = 0, where E is the shift operator.
%F a(n) = Sum_{k=0..n} (-1)^(n - k)*binomial(n, k)*(2*n + k)^(2*n + k), with 0^0 = 1.
%e The triangular array begins:
%e m: 0 1 2 3 4 5 ...
%e -------------------------------------------------------------
%e n = 0 1 1 4 27 256 ...
%e n = 1 23 40662 339512814 ...
%e n = 2 40662 339512814 ...
%e n = 3 339512814 ...
%e a(1) = 3^3 - 2^2 = 23.
%Y Cf. A000312, A395765, A069856.
%K nonn
%O 0,2
%A _Dalton Heilig_, May 18 2026