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A296374
a(0) = 3; a(n) = a(n-1)*(a(n-1)^2 - 3*a(n-1) + 4)/2.
0
3, 6, 66, 137346, 1295413937737986, 1086915296274625337063297033180803022465442306
OFFSET
0,1
COMMENTS
The next term is too large to include.
FORMULA
a(0) = 3; a(n) = [x^a(n-1)] x*(1 - 2*x + 4*x^2)/(1 - x)^4.
a(0) = 3; a(n) = a(n-1)! * [x^a(n-1)] exp(x)*x*(1 + x^2/2).
EXAMPLE
a(0) = 3;
a(1) = 6 and 6 is the 3rd triangular number;
a(2) = 66 and 66 is the 6th hexagonal number;
a(3) = 137346 and 137346 is the 66th 66-gonal number, etc.
MATHEMATICA
RecurrenceTable[{a[0] == 3, a[n] == a[n - 1] (a[n - 1]^2 - 3 a[n - 1] + 4)/2}, a[n], {n, 5}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 11 2017
STATUS
approved