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A215079
Triangle T(n,k) = k^n * sum(binomial(n,n-k-j),j=0..n-k)
2
1, 0, 1, 0, 3, 4, 0, 7, 32, 27, 0, 15, 176, 405, 256, 0, 31, 832, 3888, 6144, 3125, 0, 63, 3648, 30618, 90112, 109375, 46656, 0, 127, 15360, 216513, 1048576, 2265625, 2239488, 823543, 0, 255, 63232, 1436859, 10682368, 36328125, 62145792, 51883209, 16777216, 0, 511, 257024, 9172278, 100139008, 500000000, 1310100480, 1856265922, 1342177280, 387420489, 0, 1023, 1037312, 57159432, 889192448, 6230468750, 23339943936, 49715643824, 60129542144, 38354628411, 10000000000
OFFSET
0,5
COMMENTS
Initial term T(0,0) may be computed as 0, depending on formula and convention.
LINKS
FORMULA
T(n,k) = k^n * sum(binomial(n,n-k-j),j=0..n-k) = k^n * A055248(n,k-1).
T(n,k) = k^n * binomial(n,n-k) * 2F1(1, k-n; k+1)(-1)
T(n,1) = A000225(n). - R. J. Mathar, Feb 08 2021
EXAMPLE
1
0 1
0 3 4
0 7 32 27
0 15 176 405 256
0 31 832 3888 6144 3125
0 63 3648 30618 90112 109375 46656
0 127 15360 216513 1048576 2265625 2239488 823543
MAPLE
A215079 := proc(n, k)
k^n*add( binomial(n, n-k-j), j=0..n-k) ;
end proc: # R. J. Mathar, Feb 08 2021
MATHEMATICA
Flatten[Table[Table[Sum[k^n*Binomial[n, n - k - j], {j, 0, n - k}], {k, 0, n}], {n, 0, 10}], 1]
CROSSREFS
Row sums sequence is A215077.
Product of A055248 and A089072 (with an initial 0 in each row).
Cf. A000225 (column k=1), A000312 (diagonal).
Sequence in context: A276563 A011338 A214024 * A049251 A308642 A158674
KEYWORD
nonn,tabl
AUTHOR
Olivier Gérard, Aug 02 2012
STATUS
approved