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A099129
Let T(n) be the n-th triangular number n*(n+1)/2; then a(n) = n-th iteration T(T(T(...(n)))).
4
0, 1, 6, 231, 1186570, 347357071281165, 2076895351339769460477611370186681, 143892868802856286225154411591351342616163027795335641150249224655238508171
OFFSET
0,3
COMMENTS
The next term, a(8), has 162 digits. - Harvey P. Dale, May 29 2013
LINKS
FORMULA
a(n) = A000217^n(n).
The sequence grows like O(n^2^n*1/2^n). This can be derived from the growth O(n^2*1/2) of the triangle sum by iteration. - Hieronymus Fischer, Jan 21 2006
EXAMPLE
a(3) = 231 because we can write the 3-time iterated expression on T(3), the triangular number sequence n*(n+1)/2, namely: T(T(T(3))) = 231.
MAPLE
a:= n-> (t-> (t@@n)(n))(j-> j*(j+1)/2):
seq(a(n), n=0..7); # Alois P. Heinz, Sep 29 2023
MATHEMATICA
Table[Nest[(#(#+1))/2&, n, n], {n, 8}] (* Harvey P. Dale, May 29 2013 *)
PROG
(PARI) a(n) = my(k = n); for (j=1, n, k = k*(k+1)/2; ); k; \\ Michel Marcus, Jan 01 2017
CROSSREFS
Cf. A000217, A007501, A058009 (analog with primes), A097547.
Sequence in context: A286314 A099124 A172862 * A286392 A221926 A324232
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Nov 14 2004
EXTENSIONS
Offset changed to 1 by Georg Fischer, Jun 20 2022
a(0)=0 prepended by Alois P. Heinz, Sep 29 2023
STATUS
approved