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 A255914 Triangle read by rows: T(n,k) = A007318(n,k)*A238453(n,k). 0
 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 8, 24, 8, 1, 1, 20, 80, 80, 20, 1, 1, 12, 120, 160, 120, 12, 1, 1, 42, 252, 840, 840, 252, 42, 1, 1, 32, 672, 1344, 3360, 1344, 672, 32, 1, 1, 54, 864, 6048, 9072, 9072, 6048, 864, 54, 1, 1, 40, 1080, 5760, 30240, 18144, 30240 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS These are the generalized binomial coefficients associated with the sequence A002618. LINKS 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. FORMULA T(n,k) = Product_{i=1..n} A002618(i)/(Product_{i=1..k} A002618(i)*Product_{i=1..n-k} A002618(i)). T(n,k) = A002618(n)/n*(k/A002618(k)*T(n-1,k-1)+(n-k)/A002618(n-k)*T(n-1,k)). EXAMPLE The first five terms in A002618 (n*phi(n)) are 1, 2, 6, 8, 20 and so T(4,2) = 8*6*2*1/((2*1)*(2*1)) = 24 and T(5,3) = 20*8*6*2*1/((6*2*1)*(2*1)) = 80. The triangle begins: 1; 1, 1; 1, 2, 1; 1, 6, 6, 1; 1, 8, 24, 8, 1; 1, 20, 80, 80, 20, 1; 1, 12, 120, 160, 120, 12, 1; 1, 42, 252, 840, 840, 252, 42, 1 PROG (Sage) q=100 #change q for more rows P=[i*euler_phi(i) for i in [0..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. A002618, A238453, A007318. Sequence in context: A260238 A283795 A168641 * A143185 A157635 A075798 Adjacent sequences:  A255911 A255912 A255913 * A255915 A255916 A255917 KEYWORD nonn,tabl AUTHOR Tom Edgar, Mar 10 2015 STATUS approved

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Last modified August 6 18:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)