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

3, 6, 66, 137346, 1295413937737986, 1086915296274625337063297033180803022465442306

Offset: 0

Author

Ilya Gutkovskiy, Dec 11 2017

Keywords

• nonn

Comments

The next term is too large to include.

Examples

			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.
		

Links

• Index to sequences related to polygonal numbers

Crossrefs

Cf. A001146, A007501, A057145, A060354, A097419, A099137, A099147, A099153.

Programs

Mathematica

RecurrenceTable[{a[0] == 3, a[n] == a[n - 1] (a[n - 1]^2 - 3 a[n - 1] + 4)/2}, a[n], {n, 5}]

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).