A177812 - OEIS

%I #15 Mar 12 2014 16:37:17

%S 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 1,11,330,55,1,12,495,220,1,13,715,715,1,14,1001,2002,1,15,1365,5005,

%U 1,16,1820,11440,1,1,17,2380,24310,17,1,18,3060,48620,153

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

%C Row sums are A003099.

%e {1},

%e {1, 1},

%e {1, 2},

%e {1, 3},

%e {1, 4, 1},

%e {1, 5, 5},

%e {1, 6, 15},

%e {1, 7, 35},

%e {1, 8, 70},

%e {1, 9, 126, 1},

%e {1, 10, 210, 10}

%t Clear[t, n, m];

%t t[n_, m_] = Binomial[n, m^2];

%t Table[Table[t[n, m], {m, 0, Floor[Sqrt[n]]}], {n, 0, 10}];

%t Flatten[%]

%o (PARI) tabf(nn) = {for (n = 0, nn, for (k = 0, sqrtint(n), print1(binomial(n, k^2), ", ");); print(););} \\ _Michel Marcus_, Feb 13 2014

%Y Cf. A003099.

%K nonn,tabf

%O 0,5

%A _Roger L. Bagula_, Dec 13 2010

%E Clarified definition, changed keyword to tabf. - _N. J. A. Sloane_, Dec 16 2010

%E More terms from _Michel Marcus_, Feb 13 2014