A112503 Fourth column of triangle A112500.

1, 20, 225, 1882, 13070, 79872, 444902, 2311828, 11388999, 53820068, 246112783, 1096379070, 4782801180, 20515294320, 86808499020, 363304109640, 1507010836605, 6206407299540, 25412183425165, 103563957886370

Offset: 0

Author

Wolfdieter Lang, Oct 14 2005

Keywords

• nonn
• easy

Comments

For a combinatorial formula see A112500, case k=4.

Links

• Index entries for linear recurrences with constant coefficients, signature (20,-175,882,-2835,6072,-8777,8458,-5204,1848,-288).

Formula

G.f.: 1/product((1-j*x)^(5-j), j=1..4) = 1/(((1-x)^4)*((1-2*x)^3)*((1-3*x)^2)*(1-4*x)).

a(n) = 7813/324 + (2251/432)*(n+1) + (31/36)*binomial(n+2, 2) +(1/12)*binomial(n+3, 3) +(-1344 -256*(n+1) - 64*binomial(n+2, 2))*2^n + (6561/4 - (6561/16)*(n+1))*3^n + (32768/81)*4^n, n>=0 (from partial fractions for g.f.).