A008353 2^n*(2^(n+1) - n - 1).

1, 4, 20, 96, 432, 1856, 7744, 31744, 128768, 519168, 2085888, 8364032, 33501184, 134103040, 536625152, 2146959360, 8588820480, 34357379072, 137433972736, 549745328128, 2199001235456, 8796046884864, 35184275619840, 140737287028736, 562949533990912

Offset: 0

Author

N. J. A. Sloane and J. H. Conway

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..172
• Index entries for linear recurrences with constant coefficients, signature (8,-20,16).

Crossrefs

a(n) = A066345(2*n+1).

a(n) = 1 for n=0, 4 * A008464(n-2) else.

Programs

Magma

[2^n*(2^(n+1) - n - 1): n in [0..50]]; // Vincenzo Librandi, Apr 25 2011

PARI

Vec(-(8*x^2-4*x+1)/((2*x-1)^2*(4*x-1)) + O(x^100)) \\ Colin Barker, Feb 26 2015

Formula

a(n) = sum{k=0..n+1, C(2n+2, 2k)-2k(n-k+1)*C(n+1, k)/n}, n>0. - Paul Barry, Feb 24 2005

a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3). - Colin Barker, Feb 26 2015

G.f.: -(8*x^2-4*x+1) / ((2*x-1)^2*(4*x-1)). - Colin Barker, Feb 26 2015