A122441 Expansion of 2*(sqrt(1+8x)-3)/(sqrt(1+8x)-5).

1, -1, 1, -5, 25, -141, 849, -5349, 34825, -232445, 1582081, -10938709, 76616249, -542472685, 3876400305, -27919883205, 202480492905, -1477306676445, 10836099051105, -79861379898165, 591082795606425, -4391625157145805, 32742445489969425, -244889639907014565

Offset: 0

Author

Paul Barry, Sep 05 2006

Keywords

• easy
• sign
• changed

Links

• Robert Israel, Table of n, a(n) for n = 0..1108

Crossrefs

Row sums of A122440.

Cf. A064311.

Programs

Maple

f:= gfun:-rectoproc({(4 + 8*n)*a(n) + (-10 - 23*n)*a(n + 1) + (-3*n - 6)*a(n + 2), a(0) = 1, a(1) = -1, a(2) = 1},a(n),remember):
map(f, [$0..40]); # Robert Israel, Aug 22 2025

Sage

def a(n):
    if n==0: return 1
    return -hypergeometric([1-n, n], [-n], -2).simplify()
[a(n) for n in range(21)] # Peter Luschny, Nov 30 2014

Formula

a(n) = -hypergeometric([1-n, n], [-n], -2) if n>0. - Peter Luschny, Nov 30 2014

(4 + 8*n)*a(n) + (-10 - 23*n)*a(n + 1) + (-3*n - 6)*a(n + 2) = 0. - Robert Israel, Aug 22 2025