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%I #11 Apr 19 2013 05:48:15
%S 1,1,1,0,2,1,0,2,3,1,0,3,6,4,1,0,3,8,12,5,1,0,4,16,15,20,6,1,0,4,18,
%T 45,24,30,7,1,0,5,36,48,96,35,42,8,1,0,5,38,144,100,175,48,56,9,1,0,6,
%U 76,147,400,180,288,63,72,10,1,0,6,78,441,404,900,294,441
%N Square array T(n,k), read by antidiagonals: T(n,2*k) = T(n,2*k-1)*n, T(n,2*k+1) = T(n,2*k)+n, T(n,0) = 1.
%F T(n,0) = A000012(n).
%F T(n,1) = A000027(n).
%F T(n,2) = A002378(n+1).
%F T(n,3) = A005563(n).
%F T(n,4) = A152618(n+1).
%F T(n,5) = A045991(n+1).
%F T(n,6) = A035287(n+1).
%F T(0,k) = A019590(k+1).
%F T(1,k) = A008619(k+1).
%F T(2,k) = A123208(k).
%e Square array begins:
%e 1..1....0....0....0....0....0....0.....0.....0...
%e 1..2....2....3....3....4....4....5.....5.....5...
%e 1..3....6....8...16...18...36...38....76....78...
%e 1..4...12...15...45...48..144..147...441...444...
%e 1..5...20...24...96..100..400..404..1616..1620...
%e 1..6...30...35..175..180..900..905..4525..4530...
%e 1..7...42...48..288..294.1764.1770.10620.10626...
%e 1..8...56...63..441..448.3136.3143.22001.22008...
%e 1..9...72...80..640..648.5184.5192.41536.41544...
%e 1.10...90...99..891..900.8100.8109.72971.72980...
%e ...
%t t[n_, k_] /; n < 0 || k < 0 = 0; t[n_, 0] = 1; t[n_, 1] = n+1; t[0, k_ /; k > 1] = 0; t[n_?Positive, k_?EvenQ] := t[n, k] = t[n, k-1]*n; t[n_?Positive, k_?OddQ] := t[n, k] = t[n, k-1] + n; Table[t[n-k, k], {n, 0, 11}, {k, n, 0, -1}] // Flatten (* _Jean-François Alcover_, Apr 19 2013 *)
%K nonn,tabl
%O 0,5
%A _Philippe Deléham_, Apr 12 2013
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