1,3

Product of first n triangular numbers. Might be called a triangular factorial number. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 19 2002

Number of ways of transforming n distinguishable objects into n singletons via a sequence of n-1 refinements. Example: a(3)=3 because we have XYZ->X|YZ->X|Y|Z, XYZ->Y|XZ->X|Y|Z, and XYZ->Z|XY->X|Y|Z. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 23 2005

O. Frank and K. Svensson, On probability distributions of single-linkage dendrograms, Journal of Statistical Computation and Simulation, 12 (1981), 121-131.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 148.

P. Erdos, R. K. Guy and J. W. Moon, On refining partitions, J. London Math. Soc., 9 (1975), 565-570.

L. Lovasz, Combin. Problems and Exercises, North-Holland, 1979, p. 165.

F. Murtagh, "Counting dendrograms: a survey", Discrete Applied Mathematics, 7 (1984), 191-199.

T. D. Noe, Table of n, a(n) for n=1..50

Index entries for sequences related to factorial numbers

a(n) = a(n-1)*A000217(n).

a(n) = Polygorial(n, 3) = A000142(n)/A000079(n)*A000142(n+1) = n!/2^n*product(i+2, i=0..n-1) = n!/2^n*pochhammer(2, n) = n!^2/2^n*(n+1) = Polygorial(n, 4)/2^n*(n+1) - Daniel Dockery (peritus(AT)gmail.com) Jun 13, 2003

a(n-1) =(-1)^(n+1)/n^2/det(M_n) where M_n is the matrix M_(i, j)=abs(1/i-1/j) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 21 2003

A006472 := n->n!*(n-1)!/2^(n-1);

seq(mul(binomial(k, 2), k =2..n), n=1..18 ); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 07 2007

Cf. A084939, A084940, A084941, A084942, A084943, A084944.

Equals 2^(n-1) A010790(n-1).

Sequence in context: A080687 A111465 A108994 this_sequence A132853 A084879 A141118

Adjacent sequences: A006469 A006470 A006471 this_sequence A006473 A006474 A006475

nonn,easy,nice

njas