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%I #6 Mar 29 2015 11:35:47
%S 0,1,231,26796,1186570,26357430,359026206,3413156131,24666759216,
%T 143717956515,703974775735,2989908659661,11270904497931,
%U 38398515291136,119929709686710,347357071281165,941718655098991,2408309883851256,5847191602173306,13551450210950905
%N Quadruply triangular numbers.
%C See sequences A000217, A002817 and A064322 for triangular, doubly triangular and triply triangular numbers, respectively.
%H T. D. Noe, <a href="/A066370/b066370.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = n*(n + 1)*(n^2 + n + 2)*(n^4 + 2*n^3 + 3*n^2 + 2*n + 8)*(n^8 + 4*n^7 + 10*n^6 + 16*n^5 + 25*n^4 + 28*n^3 + 28*n^2 + 16*n + 128)/32768.
%F a(n) = A064322(n)*(A064322(n) + 1)/2 = A000217(A000217(A000217(A000217(n)))).
%e a(2)=231 as A000217(A000217(A000217(A000217(2))))=231 is the second quadruply-triangular number.
%t f[n_] := n(n + 1)/2; Table[ Nest[f, n, 4], {n, 0, 17}] (* _Robert G. Wilson v_, Jun 30 2004 *)
%K nonn
%O 0,3
%A Brian Bayerle (bbayer03(AT)providence.edu), Dec 22 2001
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