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%I #14 Sep 29 2023 19:35:51
%S 1,7,112,31192,2432305372,14790273553001687902,
%T 546880479431552932161867875823030372157,
%U 747695646958212974238278880467821187888728169501525193422768463793490256523387
%N Iterated heptagonal numbers (A000566), starting at 7.
%C The number of digits approximately doubles moving to the next member in the sequence; therefore a(8) onwards are not shown. - _R. J. Mathar_, Jun 09 2008
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>.
%F a(0, n) = 1. a(1, n) = Hep(n) = the n-th heptagonal number = n*(5*n-3)/2.
%F a(2, n) = Hep(Hep(n)) = the Hep(n)th heptagonal number = [n*(5*n-3)/2]*{5*n*(5*n-3)/2-3}/2 = (1/4)*{[Hep(n)]^2 - 3*Hep(n)}.
%F a(3, n) = Hep(Hep(Hep(n)))) = (1/8)*{125*[Hep(n)]^4 - 90*[Hep(n)]^3 + 9*[Hep(n)]^2} = (1/8)*{78125*n^8 - 187500*n^7 + 150000*n^6 - 33750*n^5 - 9375*n^4 + 3150*n^3 + 315*n^2 - 27*n}.
%F In general, a(k+1, n) = Hep[a(k, n)] = a(k, n)* [5*a(k, n)-3]/2.
%F a(n)= A000566(a(n-1)), n>1. - _R. J. Mathar_, Jun 09 2008
%e a(3) = 31192 because a(1) = the first heptagonal number = 7; a(2) = the 7th heptagonal number = 7*(5*7-3)/2 = 112; a(3) = the 112th heptagonal number = 112*(5*112-3)/2 = 31192.
%Y Cf. A007501, A000566.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Nov 15 2004
%E Corrected and extended by _R. J. Mathar_, Jun 09 2008
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