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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)))). 2
 1, 6, 231, 1186570, 347357071281165, 2076895351339769460477611370186681, 143892868802856286225154411591351342616163027795335641150249224655238508171 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The growth of this sequence is faster than exponential. This can be derived from the exponential generating function for triangular numbers: g(x) = (1 + 2x + x^2/2)*e^x = 1 + 3x/1! + 6x^2/2! + 10x^3/3! + 15x^4/4! + 21x^5/5! + ... The next term, a(8), has 162 digits. - Harvey P. Dale, May 29 2013 REFERENCES J. V. Post, "Iterated Triangular Numbers", preprint. J. V. Post, "Iterated Polygonal Numbers", preprint. LINKS FORMULA a(n) = A007501(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. 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). Sequence in context: A286314 A099124 A172862 * A286392 A221926 A324232 Adjacent sequences:  A099126 A099127 A099128 * A099130 A099131 A099132 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Nov 14 2004 STATUS approved

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Last modified September 17 17:56 EDT 2019. Contains 327136 sequences. (Running on oeis4.)