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%I #11 Feb 08 2021 07:48:30
%S 1,0,1,0,3,4,0,7,32,27,0,15,176,405,256,0,31,832,3888,6144,3125,0,63,
%T 3648,30618,90112,109375,46656,0,127,15360,216513,1048576,2265625,
%U 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
%N Triangle T(n,k) = k^n * sum(binomial(n,n-k-j),j=0..n-k)
%C Initial term T(0,0) may be computed as 0, depending on formula and convention.
%H Vincenzo Librandi, <a href="/A215079/b215079.txt">Table of n, a(n) for n = 0..1000</a>
%F T(n,k) = k^n * sum(binomial(n,n-k-j),j=0..n-k) = k^n * A055248(n,k-1).
%F T(n,k) = k^n * binomial(n,n-k) * 2F1(1, k-n; k+1)(-1)
%F T(n,1) = A000225(n). - _R. J. Mathar_, Feb 08 2021
%e 1
%e 0 1
%e 0 3 4
%e 0 7 32 27
%e 0 15 176 405 256
%e 0 31 832 3888 6144 3125
%e 0 63 3648 30618 90112 109375 46656
%e 0 127 15360 216513 1048576 2265625 2239488 823543
%p A215079 := proc(n,k)
%p k^n*add( binomial(n,n-k-j),j=0..n-k) ;
%p end proc: # _R. J. Mathar_, Feb 08 2021
%t Flatten[Table[Table[Sum[k^n*Binomial[n, n - k - j], {j, 0, n - k}], {k, 0, n}], {n, 0, 10}], 1]
%Y Row sums sequence is A215077.
%Y Product of A055248 and A089072 (with an initial 0 in each row).
%Y Cf. A000225 (column k=1), A000312 (diagonal).
%K nonn,tabl
%O 0,5
%A _Olivier Gérard_, Aug 02 2012
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