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A296374 a(0) = 3; a(n) = a(n-1)*(a(n-1)^2 - 3*a(n-1) + 4)/2.

%I A296374 #9 Dec 11 2017 14:28:45
%S A296374 3,6,66,137346,1295413937737986,
%T A296374 1086915296274625337063297033180803022465442306
%N A296374 a(0) = 3; a(n) = a(n-1)*(a(n-1)^2 - 3*a(n-1) + 4)/2.
%C A296374 The next term is too large to include.
%H A296374 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F A296374 a(0) = 3; a(n) = [x^a(n-1)] x*(1 - 2*x + 4*x^2)/(1 - x)^4.
%F A296374 a(0) = 3; a(n) = a(n-1)! * [x^a(n-1)] exp(x)*x*(1 + x^2/2).
%e A296374 a(0) = 3;
%e A296374 a(1) = 6 and 6 is the 3rd triangular number;
%e A296374 a(2) = 66 and 66 is the 6th hexagonal number;
%e A296374 a(3) = 137346 and 137346 is the 66th 66-gonal number, etc.
%t A296374 RecurrenceTable[{a[0] == 3, a[n] == a[n - 1] (a[n - 1]^2 - 3 a[n - 1] + 4)/2}, a[n], {n, 5}]
%Y A296374 Cf. A001146, A007501, A057145, A060354, A097419, A099137, A099147, A099153.
%K A296374 nonn
%O A296374 0,1
%A A296374 _Ilya Gutkovskiy_, Dec 11 2017