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A167034
Triangle t(n,m)= (m+1)^n*binomial(n,m) if m <= n/2, otherwise t(n,m) = t(n,n-m).
1
1, 1, 1, 1, 8, 1, 1, 24, 24, 1, 1, 64, 486, 64, 1, 1, 160, 2430, 2430, 160, 1, 1, 384, 10935, 81920, 10935, 384, 1, 1, 896, 45927, 573440, 573440, 45927, 896, 1, 1, 2048, 183708, 3670016, 27343750, 3670016, 183708, 2048, 1, 1, 4608, 708588, 22020096
OFFSET
0,5
COMMENTS
Row sums are 1, 2, 10, 50, 616, 5182, 104560, 1240528, 35055296, 537654086, 19596031984,...
This is obtained by taking the absolute value of the first half of each row of A075513 and defining the second half by mirror symmetry.
EXAMPLE
1;
1, 1;
1, 8, 1;
1, 24, 24, 1;
1, 64, 486, 64, 1;
1, 160, 2430, 2430, 160, 1;
1, 384, 10935, 81920, 10935, 384, 1;
1, 896, 45927, 573440, 573440, 45927, 896, 1;
1, 2048, 183708, 3670016, 27343750, 3670016, 183708, 2048, 1;
MAPLE
A167034 := proc(n, m)
if m <= n/2 then
(m+1)^n*binomial(n, m) ;
else
procname(n, n-m) ;
end if;
end proc: # R. J. Mathar, Oct 13 2012
MATHEMATICA
T[m_, n_] = If[Floor[m/2] >= n, (n + 1)^m*Binomial[m, n], (m - n + 1)^m*Binomial[m, m - n]]
Flatten[Table[Table[T[m, n], {n, 0, m}], {m, 0, 10}]]
CROSSREFS
Sequence in context: A176488 A144436 A358628 * A155452 A147295 A174388
KEYWORD
nonn,easy,tabl
AUTHOR
Roger L. Bagula and Mats Granvik, Oct 27 2009
STATUS
approved