OFFSET
1,2
LINKS
Alois P. Heinz, Rows n = 1..65, flattened
Wikipedia, Standard deviation
EXAMPLE
Triangle T(n,k) begins:
1;
2;
3;
4, 1;
6, 1;
8, 2, 1;
10, 4, 1;
12, 7, 2, 1;
15, 10, 4, 1;
19, 14, 6, 2, 1;
23, 21, 7, 4, 1;
25, 32, 14, 3, 2, 1;
MAPLE
b:= proc(n, i, m, s, c) `if`(n=0, x^floor(sqrt(s/c-(m/c)^2)),
`if`(i=1, b(0$2, m+n, s+n, c+n), add(b(n-i*j, i-1,
m+i*j, s+i^2*j, c+j), j=0..n/i)))
end:
T:= n->(p->seq(coeff(p, x, i), i=0..degree(p)))(b(n$2, 0$3)):
seq(T(n), n=1..18);
MATHEMATICA
b[n_, i_, m_, s_, c_] := b[n, i, m, s, c] = If[n==0, x^Floor[Sqrt[s/c - (m/c)^2]], If[i==1, b[0, 0, m+n, s+n, c+n], Sum[b[n-i*j, i-1, m+i*j, s + i^2*j, c+j], {j, 0, n/i}]]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n, n, 0, 0, 0]]; Table[T[n], {n, 1, 18}] // Flatten (* Jean-François Alcover, Nov 17 2015, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Mar 12 2014
STATUS
approved