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A364812
Triangle of generalized binomial coefficients T(n,k) = ff(n)/(ff(k)*ff(n-k)) where ff(n) = A363838(n), the generalized factorial.
1
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 16, 24, 16, 1, 1, 5, 40, 40, 5, 1, 1, 36, 90, 480, 90, 36, 1, 1, 7, 126, 210, 210, 126, 7, 1, 1, 256, 896, 10752, 3360, 10752, 896, 256, 1, 1, 81, 10368, 24192, 54432, 54432, 24192, 10368, 81, 1, 1, 100, 4050, 345600, 151200, 1088640, 151200, 345600, 4050, 100, 1
OFFSET
0,5
LINKS
Michel Marcus, Table of n, a(n) for n = 0..5150 (Rows n=0..100 flattened).
Jeffrey C. Lagarias and Wijit Yangjit, The factorial function and generalizations, extended, arXiv:2310.12949 [math.NT], 2023. See Table 3 p. 30.
FORMULA
T(n,k) = A363838(n)/(A363838(k)*A363838(n-k)).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 16, 24, 16, 1;
1, 5, 40, 40, 5, 1;
1, 36, 90, 480, 90, 36, 1;
...
PROG
(PARI)
f(n, b) = sum(i=1, logint(n, b), n\b^i);
ff(n) = prod(b=2, n, b^f(n, b)); \\ A363838
T(n, k) = ff(n)/(ff(k)*ff(n-k));
row(n) = vector(n+1, k, T(n, k-1));
CROSSREFS
Sequence in context: A129439 A176469 A141542 * A129453 A129455 A329322
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Oct 21 2023
STATUS
approved