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%I #40 Apr 29 2020 10:01:20
%S 1,0,1,1,0,1,1,0,1,1,0,1,1,1,1,1,1,0,1,1,0,1,1,1,2,1,2,1,2,1,1,1,0,1,
%T 1,0,1,1,1,2,2,2,2,3,2,3,2,2,2,2,1,1,1,0,1,1,0,1,1,1,2,2,3,2,4,3,4,4,
%U 4,4,4,4,3,4,2,3,2,2,1,1,1,0,1
%N Irregular triangle read by rows: T(n,k) is the number of partitions of k into distinct parts p such that 2 <= p <= n.
%F G.f. for row n: Product_{i=2..n} (1+x^i), n >= 2.
%e Irregular triangle begins:
%e ----------------------------------------------------------
%e n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
%e ----------------------------------------------------------
%e 2 | 1 0 1
%e 3 | 1 0 1 1 0 1
%e 4 | 1 0 1 1 1 1 1 1 0 1
%e 5 | 1 0 1 1 1 2 1 2 1 2 1 1 1 0 1
%e 6 | 1 0 1 1 1 2 2 2 2 3 2 3 2 2 2 2 1 1 1 0 1
%e ...
%e For n = 4: T(4,3) = 1 because we have [3], G.f.=1+x^2+x^3+x^4+x^5+x^6+x^7+x^9;
%e For n = 5: T(5,5) = 2 because we have [5] and [3,2].
%e G.f. is 1+x^2+x^3+x^4+2x^5+x^6+2x^7+x^8+2x^9+x^10+x^11+x^12+x^14.
%t trow[n_] := CoefficientList[Product[(1 + x^i), {i, 2, n}], x]; nmax = 10; Table[trow[n], {n, 2, nmax}] // Flatten
%Y Cf. A000009, A000041, A025147, A087897, A334305.
%K tabf,nonn,easy
%O 2,25
%A Victor Mishnyakov, _Elena Lanina_, Apr 25 2020
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