A109957 Diagonal sums of number triangle A109956.

1, -1, 4, -16, 74, -368, 1926, -10455, 58333, -332489, 1927761, -11334128, 67416570, -404956315, 2453012916, -14967587873, 91910798556, -567566697627, 3522334450512, -21957276973619, 137425078658354, -863229921626723, 5440215989173113, -34388244134246836

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: g/(1-x^2*g^3) where f/(1-f)^3=x and g=1-f. [Corrected by Seiichi Manyama, Nov 27 2025]

a(n) = (-1)^n * Sum_{k=0..floor(n/2)} ((3*k+1)/(2*n-k+1)) * binomial(3*n-3*k, n-2*k).

Crossrefs

Cf. A109956, A109963, A179848.

Sequence in context: A301455 A214372 A366495 * A394946 A366498 A306495

Adjacent sequences: A109954 A109955 A109956 * A109958 A109959 A109960

Keyword

easy,sign

Author

Paul Barry, Jul 06 2005

Status

approved