OFFSET
0,12
COMMENTS
LINKS
Tom Edgar, Totienomial Coefficients, INTEGERS, 14 (2014), #A62.
Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.
Donald E. Knuth and Herbert S. Wilf, The power of a prime that divides a generalized binomial coefficient, J. Reine Angew. Math., 396:212-219, 1989.
FORMULA
EXAMPLE
The first five terms in A003557 are: 1, 1, 1, 2, 1 and so T(4,2) = 2*1*1*1/((1*1)*(1*1))=2 and T(5,4) = 1*2*1*1*1/((2*1*1*1)*(1))=1.
The triangle begins:
1,
1, 1,
1, 1, 1,
1, 1, 1, 1,
1, 2, 2, 2, 1,
1, 1, 2, 2, 1, 1,
1, 1, 1, 2, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1,
1, 4, 4, 4, 2, 4, 4, 4, 1,
1, 3, 12, 12, 6, 6, 12, 12, 3, 1.
PROG
(Sage)
q=100 #change q for more rows
P=[0]+[n/prod([x for x in prime_divisors(n)]) for n in [1..q]]
[[prod(P[1:n+1])/(prod(P[1:k+1])*prod(P[1:(n-k)+1])) for k in [0..n]] for n in [0..len(P)-1]] # generates the triangle up to q rows.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Tom Edgar, Aug 27 2014
STATUS
approved