OFFSET
0,5
COMMENTS
If one starts the sum at j=0, the initial term T(0,0) is 1.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
T(n,k) = binomial(n,k)*sum(j^n, j=1..k)
EXAMPLE
0
0 1
0 2 5
0 3 27 36
0 4 102 392 354
0 5 330 2760 6500 4425
0 6 975 15880 73350 123090 67171
0 7 2709 81060 654500 2033325 2637327 1200304
MAPLE
A215078 := proc(n, k)
binomial(n, k)*add(j^n, j=1..k) ;
end proc:
seq(seq(A215078(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Jan 27 2023
MATHEMATICA
Flatten[Table[Table[Sum[j^n, {j, 1, k}]*Binomial[n, k], {k, 0, n}], {n, 0, 10}], 1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Olivier Gérard, Aug 02 2012
STATUS
approved