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Number of integers m, 1 <= m <= A002569(n), that are not terms in the triangle T(n,k) of A008284.
0

%I #16 Oct 01 2017 00:44:47

%S 0,0,0,0,0,0,0,0,0,0,0,1,2,4,6,8,12,19,26,39,52,71,92,120,161,205,258,

%T 320,398,499,613,754,911,1103,1340,1622,1956,2338,2789,3303,3938,4690,

%U 5547,6551,7690,9018,10584,12425,14559,16989,19790,22970,26615

%N Number of integers m, 1 <= m <= A002569(n), that are not terms in the triangle T(n,k) of A008284.

%e With n = 10, the maximum value of m is 9 and all values of m from 1 to 9 appear within the first 10 rows of A008284, so a(10) = 0.

%e With n = 13, the maximum value of m is 18 and all values of m from 1 to 18, except 16 and 17, appear within the first 13 rows of A008284, so a(13) = 2.

%t FoldList[{#1, Count[Range@ Max@ #2, k_ /; FreeQ[#1, k]]} & @@ {Append[#1, #2], #2} & @@ {First@ #1, Table[SeriesCoefficient[1/QPochhammer[a q, q], {q, 0, #2}, {a, 0, k}], {k, #2}]} &, {{{1}}, 0}, Range[2, 40]][[All, -1]] (* _Michael De Vlieger_, Sep 29 2017, after _Vladimir Reshetnikov_ at A008284 *)

%Y Cf. A008284, A002569.

%K nonn

%O 1,13

%A _J. Stauduhar_, Sep 28 2017