A055250 Seventh column of triangle A055249.
1, 9, 47, 187, 630, 1898, 5282, 13866, 34831, 84575, 199977, 462973, 1053804, 2365704, 5250660, 11543700, 25177005, 54539205, 117456115, 251676495, 536892146, 1140875254, 2415947382, 5100306062, 10737455195, 22548620283
Offset: 0
Programs
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Maple
a:= n-> (Matrix(7, (i,j)-> if (i=j-1) then 1 elif j=1 then [9,-34,70,-85,61,-24,4][i] else 0 fi)^(n))[1,1]: seq(a(n), n=0..25); # Alois P. Heinz, Aug 05 2008
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Mathematica
Table[Sum[(-1)^(n - k) k (-1)^(n - k) Binomial[n + 5, k + 5], {k, 0, n}], {n, 1, 26}] (* Zerinvary Lajos, Jul 08 2009 *)
Formula
G.f.: 1/(((1-2*x)^2)*(1-x)^5).
a(n) = A055249(n+6, 6).
For n >= 1, a(n) = A035038(n+6) + Sum_{j=0..n-1} a(j).
a(n) = Sum_{k=0..n+5} Sum_{i=0..n+5} (i-k) * C(n-k+5,i+3). - Wesley Ivan Hurt, Sep 19 2017