A397449 - OEIS

A397449

a(n) = Sum_{k=0..n-1} a(k)*(-2)^k, with a(0) = 1.

1, 1, -1, -5, 35, 595, -18445, -1198925, 152263475, 39131713075, -19996305381325, -20496213015858125, 41955748043461581875, 171892699734062100941875, -1407973103521702668814898125, -23069639301203098228532105778125, 755922870982521919654311510031821875

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Up to sign the denominators in the Engel-type expansion given by Peter Bala in A014551.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) = Product_{k=2..n} ((-2)^(k-1)+1).

a(n+1)/a(n) = A014551(n)*(-1)^n, for n > 0.

a(n) = QPochhammer(1/2; -2)_{n+1}, for n > 0, where QPochhammer is the q-analog of the Pochhammer symbol: (a; q)_n.

Sum_{k>=0} (-2)^k/a(k) = -3.