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A369381
Triangle of numbers read by rows T(n,k) = binomial(n+1,k+1)*Stirling2(n+k,k).
0
1, 0, 1, 0, 3, 7, 0, 6, 60, 90, 0, 10, 310, 1505, 1701, 0, 15, 1260, 14490, 46620, 42525, 0, 21, 4445, 105875, 716205, 1727110, 1323652, 0, 28, 14280, 653100, 8162000, 38623200
OFFSET
0,5
COMMENTS
The triangle T(n,k) is a functional dual of the triangle A269939 in identity: B(n) = Sum_{k=0..n}(-1)^(k)*A269939(n,k)/Binomial(n+k,k) = Sum_{k=0..n}(-1)^(k)*T(n,k)/Binomial(n+k,k). Where B(n) are the Bernoulli numbers.
LINKS
I. V. Statsenko, Functional twin of triangle A269939, Innovation science No 1-2, State Ufa, Aeterna Publishing House, 2024, pp. 15-19. In Russian.
FORMULA
T(n,k) = binomial(n+1,k+1)*Stirling2(n+k,k).
EXAMPLE
n\k 0 1 2 3 4 5
0: 1
1: 0 1
2: 0 3 7
3: 0 6 60 90
4: 0 10 310 1505 1701
5: 0 15 1260 14490 46620 42525
MAPLE
T:=(n, k)->((n+1)!/((k+1)!*(n-k)!))*Stirling2(n+k, k):seq(seq T(n, k), k=0..n), n=0..10);
CROSSREFS
Cf. A007820 (right diagonal).
Sequence in context: A197835 A197005 A199778 * A086729 A332527 A175576
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved