This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A238754 Triangle read by rows: T(n,k) = A059383(n)/(A059383(k)*A059383(n-k)). 2
 1, 1, 1, 1, 15, 1, 1, 80, 80, 1, 1, 240, 1280, 240, 1, 1, 624, 9984, 9984, 624, 1, 1, 1200, 49920, 149760, 49920, 1200, 1, 1, 2400, 192000, 1497600, 1497600, 192000, 2400, 1, 1, 3840, 614400, 9216000, 23961600, 9216000, 614400, 3840, 1, 1, 6480, 1658880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS We assume that A059383(0)=1 since it would be the empty product. These are the generalized binomial coefficients associated with the Jordan totient function J_4 given in A059377. Another name might be the 4-totienomial coefficients. 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 T(n,k) = A059383(n)/(A059383(k)* A059383(n-k)). T(n,k) = prod_{i=1..n} A059377(i)/(prod_{i=1..k} A059377(i)*prod_{i=1..n-k} A059377(i)). T(n,k) = A059377(n)/n*(k/A059377(k)*T(n-1,k-1)+(n-k)/A059377(n-k)*T(n-1,k)). EXAMPLE The first five terms in the fourth Jordan totient function are 1,15,80,240,624 and so T(4,2) = 240*80*15*1/((15*1)*(15*1))=1280 and T(5,3) = 624*240*80*15*1/((80*15*1)*(15*1))=9984. The triangle begins 1 1 1 1 15  1 1 80  80   1 1 240 1280 240  1 1 624 9984 9984 624 1 PROG (Sage) q=100 #change q for more rows P=[0]+[i^4*prod([1-1/p^4 for p in prime_divisors(i)]) for i 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 Cf. A059377, A059383,  A238453, A238688, A238743. Sequence in context: A174389 A176286 A111805 * A176226 A155493 A156939 Adjacent sequences:  A238751 A238752 A238753 * A238755 A238756 A238757 KEYWORD nonn,tabl AUTHOR Tom Edgar, Mar 04 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 16 06:21 EDT 2019. Contains 327090 sequences. (Running on oeis4.)