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A304330
T(n, k) = Sum_{j=0..k} (-1)^j*binomial(2*k, j)*(k - j)^(2*n), triangle read by rows, n >= 0 and 0 <= k <= n.
8
1, 0, 1, 0, 1, 12, 0, 1, 60, 360, 0, 1, 252, 5040, 20160, 0, 1, 1020, 52920, 604800, 1814400, 0, 1, 4092, 506880, 12640320, 99792000, 239500800, 0, 1, 16380, 4684680, 230630400, 3632428800, 21794572800, 43589145600, 0, 1, 65532, 42653520, 3952428480
OFFSET
0,6
LINKS
José L. Cereceda, Sums of powers of integers and the sequence A304330, arXiv:2405.05268 [math.GM], 2024.
EXAMPLE
Triangle starts:
[0] 1;
[1] 0, 1;
[2] 0, 1, 12;
[3] 0, 1, 60, 360;
[4] 0, 1, 252, 5040, 20160;
[5] 0, 1, 1020, 52920, 604800, 1814400;
[6] 0, 1, 4092, 506880, 12640320, 99792000, 239500800;
[7] 0, 1, 16380, 4684680, 230630400, 3632428800, 21794572800, 43589145600;
MAPLE
T := (n, k) -> add((-1)^j*binomial(2*k, j)*(k-j)^(2*n), j=0..k):
for n from 0 to 8 do seq(T(n, k), k=0..n) od;
CROSSREFS
Row sums are A100872, T(n,2) = A058896, T(n,n) = A002674, T(n,n-1)= A091032.
Sequence in context: A156401 A246223 A199542 * A322731 A370330 A370430
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 11 2018
STATUS
approved