A177812 Triangular array read by rows: binomial(n,k^2), k=0..floor(sqrt(n)).
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, 1, 11, 330, 55, 1, 12, 495, 220, 1, 13, 715, 715, 1, 14, 1001, 2002, 1, 15, 1365, 5005, 1, 16, 1820, 11440, 1, 1, 17, 2380, 24310, 17, 1, 18, 3060, 48620, 153
Offset: 0
Examples
{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}
Crossrefs
Cf. A003099.
Programs
-
Mathematica
Clear[t, n, m]; t[n_, m_] = Binomial[n, m^2]; Table[Table[t[n, m], {m, 0, Floor[Sqrt[n]]}], {n, 0, 10}]; Flatten[%] -
PARI
tabf(nn) = {for (n = 0, nn, for (k = 0, sqrtint(n), print1(binomial(n, k^2), ", ");); print(););} \\ Michel Marcus, Feb 13 2014
Extensions
Clarified definition, changed keyword to tabf. - N. J. A. Sloane, Dec 16 2010
More terms from Michel Marcus, Feb 13 2014
Comments