A174016 Row sums of number triangle A174014.

1, 2, 6, 16, 40, 92, 192, 352, 528, 512, -192, -2128, -3840, 5888, 69056, 299264, 917760, 2125184, 3258368, -117760, -23297536, -103321600, -295843840, -577744128, -416948224, 2490589184, 14821469184, 50063536128

Offset: 0

Author

Paul Barry, Mar 05 2010

Keywords

• easy
• sign

Comments

Hankel transform is 1, 2, -8, -32, -256, 4096, ... (signed version of A134751).

Formula

G.f.: (sqrt(1-4x+4x^2+8x^3)+4x-1)/(2x(1-2x));

g.f.: 1/(1-2x/(1-x/(1+x/(1-2x/(1-x/(1+x/(1-2x/(1-... (continued fraction).

a(n) = Sum_{k=0..n} A198379(n,k)*2^k. - Philippe Deléham, Oct 29 2011

Conjecture: (n+1)*a(n) - 6*n*a(n-1) + 12*(n-1)*a(n-2) - 12*a(n-3) + 8*(7-2*n)*a(n-4) = 0. - R. J. Mathar, Nov 13 2012

Extensions

First formula corrected by Philippe Deléham, Feb 16 2012