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A177517 Triangle T(n,k) read by rows defined by recurrence T(n,1)=A000007(n-1) and T(n,k) = sum_{i=1..k-1} T(n-i,k-1) if k>1.

%I A177517 #29 Dec 26 2023 00:15:20
%S A177517 1,0,1,0,0,1,0,0,1,1,0,0,0,2,1,0,0,0,2,3,1,0,0,0,1,5,4,1,0,0,0,0,6,9,
%T A177517 5,1,0,0,0,0,5,15,14,6,1,0,0,0,0,3,20,29,20,7,1,0,0,0,0,1,22,49,49,27,
%U A177517 8,1,0,0,0,0,0,20,71,98,76,35,9,1,0,0,0,0,0,15,90,169,174,111,44,10,1,0,0,0,0,0,9,101,259,343,285,155,54,11,1,0,0,0,0,0,4,101,359,602,628,440,209,65,12,1,0,0,0,0,0,1,90,455,961,1230,1068,649,274,77,13,1
%N A177517 Triangle T(n,k) read by rows defined by recurrence T(n,1)=A000007(n-1) and T(n,k) = sum_{i=1..k-1} T(n-i,k-1) if k>1.
%C A177517 A008302 is the main entry for this triangle.
%C A177517 Essentially A060701 which is equal to this table beginning from the second column.
%C A177517 The recurrence formula is similar to the recurrence for A177978.
%H A177517 Alois P. Heinz, <a href="/A177517/b177517.txt">Table of n, a(n) for n = 1..20301</a>
%F A177517 T(n,k) = A008302(k-2,n-k), n>=k>1. - _R. J. Mathar_, Dec 15 2010
%e A177517 1,
%e A177517 0,1,
%e A177517 0,0,1,
%e A177517 0,0,1,1,
%e A177517 0,0,0,2,1,
%e A177517 0,0,0,2,3,1,
%e A177517 0,0,0,1,5,4,1,
%e A177517 0,0,0,0,6,9,5,1,
%e A177517 0,0,0,0,5,15,14,6,1,
%e A177517 0,0,0,0,3,20,29,20,7,1,
%e A177517 0,0,0,0,1,22,49,49,27,8,1
%t A177517 t[1, 1] = 1; t[n_, 1] = 0; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}], 0];
%t A177517 Flatten[Table[t[n, k], {n, 12}, {k, n}]]
%t A177517 (* _Robert G. Wilson v_, Jun 24 2011 *) (* corrected by _Mats Granvik_, Jan 23 2012 *)
%Y A177517 Cf. A008302, A060701, A177978, A175105. Column sums are A000142. Row sums are A008930.
%K A177517 nonn,tabl
%O A177517 1,14
%A A177517 _Mats Granvik_, _Roger L. Bagula_, Dec 11 2010