A112502 Third column of triangle A112500.

1, 10, 60, 282, 1149, 4272, 14932, 49996, 162369, 515886, 1613316, 4987542, 15290461, 46592452, 141350412, 427459320, 1289718225, 3884883570, 11688205420, 35135919730, 105558754461, 316995030840, 951656181540

Offset: 0

Author

Wolfdieter Lang, Oct 14 2005

Keywords

• nonn
• easy

Comments

For a combinatorial formula see A112500, case k=3.

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).

Crossrefs

Cf. A000295 (second column).

Formula

G.f.: 1/product((1-j*x)^(4-j), j=1..3) = 1/(((1-x)^3)*((1-2*x)^2)*(1-3*x)).

a(n) = - 81/8 - (11/4)*(n+1) - (1/2)*binomial(n+2, 2) - 16*(n+1)*2^n + (243/8)*3^n, n>=0 (from partial fractions for g.f.).