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%I #12 Mar 08 2023 11:48:59
%S 1,-6,55,-736,13573,-330058,10233219,-393999940,18443289777,
%T -1031520165710,67934648699151,-5203713576558056,458704384454574365,
%U -46104659405475675026,5241286859201262537563,-669127269362962909934028,95322254316544433430632009
%N Fourth column of Salié-triangle A065547.
%F a(n) = A065547(n+3, 3), n>=0.
%t col = 4; nmax = 16; h[n_, x_] := Sum[c[k]*x^k, {k, 0, n}]; eq[n_] := SolveAlways[h[n, x*(x - 1)] == EulerE[2*n, x], x]; row[n_] := Table[c[k], {k, 0, n}] /. eq[n] // First; A065547 = Table[row[n], {n, 0, nmax + col}]; a[n_] := A065547[[n + col, col]]; Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Oct 02 2013 *)
%Y Cf. A065547.
%K sign,easy
%O 0,2
%A _Wolfdieter Lang_, Jun 11 2004