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A128814 a(0)=1, a(n)= Product(k*(k+1)/2+1, k=1..n). 0
1, 2, 8, 56, 616, 9856, 216832, 6288128, 232660736, 10702393856, 599334055936, 40155381747712, 3172275158069248, 291849314542370816, 30936027341491306496, 3743259308320448086016, 512826525239901387784192 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial products of A000124.

LINKS

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

FORMULA

a(n) grows roughly like (n!)^2/2^n.

G.f.: G(0)/(2*x^2) - 1/x^2 - 1/x, where G(k)= 1 + 1/(1 - x*(k^2-k+2)/(x*(k^2-k+2) + 2/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 18 2013

a(n) = -2^(-n-1)*Gamma(n+3/2+sqrt(-7)/2)*Gamma(n+3/2-sqrt(-7)/2)*sin((3+sqrt(-7))*pi/2)/pi. - Robert Israel, May 19 2014

MAPLE

a[0]:=1:for n from 1 to 20 do a[n]:=product(k*(k+1)/2+1, k=1..n) od: seq(a[n], n=0..20);

CROSSREFS

Cf. A000142, A006472.

Sequence in context: A197949 A243953 A005439 * A108208 A203199 A348875

Adjacent sequences:  A128811 A128812 A128813 * A128815 A128816 A128817

KEYWORD

easy,nonn

AUTHOR

Miklos Kristof, Apr 10 2007

STATUS

approved

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Last modified May 18 19:51 EDT 2022. Contains 353824 sequences. (Running on oeis4.)