A142966 Fourth column (m=3) of triangle A142963 divided by 8.

1, 58, 877, 8030, 56285, 335162, 1792749, 8904486, 41949645, 190129090, 837258109, 3607669966, 15289404989, 63975698570, 265065915725, 1089837752118, 4454225465325, 18119738464530, 73441531708765, 296814738679390, 1196884383319261, 4817845684107098

Offset: 0

Author

Wolfdieter Lang, Sep 15 2008

Keywords

• nonn
• easy

Crossrefs

Cf. A142963.

Column m=2: 4*A142965.

From Johannes W. Meijer, Feb 20 2009: (Start)

Cf. A156925.

Equals A156920(n+3,3).

Equals A156919(n+3,3)/2^n.

(End)

Formula

a(n) = A142963(n+4,3)/8.

From Johannes W. Meijer, Feb 20 2009: (Start)

a(n) = 20a(n-1) - 175*a(n-2) + 882*a(n-3) - 2835*a(n-4) + 6072*a(n-5) - 8777*a(n-6) + 8458*a(n-7) - 5204*a(n-8) + 1848*a(n-9) - 288*a(n-10).

a(n) = -(105/2) - (143/3)*n - 14*n^2 - (4/3)*n^3 + 756*2^n + 48*2^n*n^2 + 384*2^n*n - (3645/2)*3^n - 405*3^n*n + 1120*4^n.

G.f.: (1 + 38*z - 108*z^2 - 242*z^3 + 839*z^4 - 444*z^5 - 180*z^6)/((1-z)^4*(1-2*z)^3*(1-3*z)^2*(1-4*z)).

(End)