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A112503 Fourth column of triangle A112500. 2

%I #3 Oct 12 2012 14:40:24

%S 1,20,225,1882,13070,79872,444902,2311828,11388999,53820068,246112783,

%T 1096379070,4782801180,20515294320,86808499020,363304109640,

%U 1507010836605,6206407299540,25412183425165,103563957886370

%N Fourth column of triangle A112500.

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

%F 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)).

%F 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.).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 14 2005

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