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, 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.

Links

Table of n, a(n) for n=0..48.

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

Adjacent sequences: A167031 A167032 A167033 * A167035 A167036 A167037

Keyword

nonn,easy,tabl

Author

Roger L. Bagula and Mats Granvik, Oct 27 2009

Status

approved