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A177812 Triangular array read by rows: binomial(n,k^2), k=0..floor(sqrt(n)).

%I A177812 #15 Mar 12 2014 16:37:17
%S A177812 1,1,1,1,2,1,3,1,4,1,1,5,5,1,6,15,1,7,35,1,8,70,1,9,126,1,1,10,210,10,
%T A177812 1,11,330,55,1,12,495,220,1,13,715,715,1,14,1001,2002,1,15,1365,5005,
%U A177812 1,16,1820,11440,1,1,17,2380,24310,17,1,18,3060,48620,153
%N A177812 Triangular array read by rows: binomial(n,k^2), k=0..floor(sqrt(n)).
%C A177812 Row sums are A003099.
%e A177812 {1},
%e A177812 {1, 1},
%e A177812 {1, 2},
%e A177812 {1, 3},
%e A177812 {1, 4, 1},
%e A177812 {1, 5, 5},
%e A177812 {1, 6, 15},
%e A177812 {1, 7, 35},
%e A177812 {1, 8, 70},
%e A177812 {1, 9, 126, 1},
%e A177812 {1, 10, 210, 10}
%t A177812 Clear[t, n, m];
%t A177812 t[n_, m_] = Binomial[n, m^2];
%t A177812 Table[Table[t[n, m], {m, 0, Floor[Sqrt[n]]}], {n, 0, 10}];
%t A177812 Flatten[%]
%o A177812 (PARI) tabf(nn) = {for (n = 0, nn, for (k = 0, sqrtint(n), print1(binomial(n, k^2), ", ");); print(););} \\ _Michel Marcus_, Feb 13 2014
%Y A177812 Cf. A003099.
%K A177812 nonn,tabf
%O A177812 0,5
%A A177812 _Roger L. Bagula_, Dec 13 2010
%E A177812 Clarified definition, changed keyword to tabf. - _N. J. A. Sloane_, Dec 16 2010
%E A177812 More terms from _Michel Marcus_, Feb 13 2014