Triangle of up-down sums of k-th powers: a(n,k)=sum(i^k,i=1..n)+sum((n-i)^k,i=1..n-1), n,k>0.

Terms

a(0) =1a(1) =4a(2) =1a(3) =9a(4) =6a(5) =1a(6) =16a(7) =19a(8) =10a(9) =1a(10) =25a(11) =44a(12) =45a(13) =18a(14) =1a(15) =36a(16) =85a(17) =136a(18) =115a(19) =34a(20) =1a(21) =49a(22) =146a(23) =325a(24) =452a(25) =309a(26) =66a(27) =1a(28) =64a(29) =231