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 A203309 Vandermonde determinant of the first n triangular numbers. 4
 1, 2, 30, 7560, 57153600, 20369543040000, 495474875767872000000, 1124860755259775229696000000000, 312577210159744965479388971827200000000000, 13502658421660070413446616883411391637094400000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Each term divides its successor, as in A203310. LINKS MAPLE with(LinearAlgebra): a:= n-> Determinant(VandermondeMatrix([i*(i+1)/2\$i=1..n])): seq(a(n), n=1..12);  # Alois P. Heinz, Jul 23 2017 MATHEMATICA f[j_] := j (j + 1)/2; z = 15; v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}] Table[v[n], {n, 1, z}]   (* A203309 *) Table[v[n + 1]/v[n], {n, 1, z - 1}]  (* A203310 *) PROG (Python) from operator import mul def f(n): return n*(n + 1)/2 def v(n): return 1 if n==1 else reduce(mul, [reduce(mul, [f(k) - f(j) for j in xrange(1, k)]) for k in xrange(2, n + 1)]) print map(v, xrange(1, 11)) # Indranil Ghosh, Jul 24 2017 CROSSREFS Cf. A203310. Sequence in context: A053851 A077521 A272445 * A090600 A113511 A292048 Adjacent sequences:  A203306 A203307 A203308 * A203310 A203311 A203312 KEYWORD nonn AUTHOR Clark Kimberling, Jan 01 2012 STATUS approved

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Last modified September 25 02:13 EDT 2017. Contains 292441 sequences.