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A329820
Triangular array, read by rows: T(n,k) = [(w*x*y*z)^k] (-1 + (1 + w + 1/w)*(1 + x + 1/x)*(1 + y + 1/y)*(1 + z + 1/z))^n for -n <= k <= n.
2
1, 1, 0, 1, 1, 14, 80, 14, 1, 1, 78, 1251, 2160, 1251, 78, 1, 1, 252, 9682, 60444, 121200, 60444, 9682, 252, 1, 1, 620, 49355, 760800, 3785750, 6136800, 3785750, 760800, 49355, 620, 1, 1, 1290, 190746, 5950070, 60898395, 228400980, 356570960, 228400980, 60898395, 5950070, 190746, 1290, 1
OFFSET
0,6
FORMULA
T(n,k) = T(n,-k).
EXAMPLE
Triangle begins:
1;
1, 0, 1;
1, 14, 80, 14, 1;
1, 78, 1251, 2160, 1251, 78, 1;
1, 252, 9682, 60444, 121200, 60444, 9682, 252, 1;
PROG
(PARI) {T(n, k) = polcoef(polcoef(polcoef(polcoef((-1+(1+w+1/w)*(1+x+1/x)*(1+y+1/y)*(1+z+1/z))^n, k), k), k), k)}
CROSSREFS
T(n,0) gives A328875.
Sequence in context: A231241 A138401 A099360 * A239421 A309338 A215472
KEYWORD
nonn,tabf
AUTHOR
Seiichi Manyama, Nov 21 2019
STATUS
approved