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A098436
Triangle of 3rd central factorial numbers T(n,k).
3
1, 1, 1, 1, 9, 1, 1, 73, 36, 1, 1, 585, 1045, 100, 1, 1, 4681, 28800, 7445, 225, 1, 1, 37449, 782281, 505280, 35570, 441, 1, 1, 299593, 21159036, 33120201, 4951530, 130826, 784, 1, 1, 2396745, 571593565, 2140851900, 652061451, 33209946, 399738, 1296, 1
OFFSET
0,5
LINKS
FORMULA
Recurrence: T(n, k) = k^3*T(n-1, k) + T(n-1, k-1), T(0, 0)=1.
EXAMPLE
1;
1, 1;
1, 9, 1;
1, 73, 36, 1;
1, 585, 1045, 100, 1;
...
MATHEMATICA
T[n_, n_] = 1;
T[n_ /; n>=0, k_] /; 0<=k<=n := T[n, k] = (k+1)^3 T[n-1, k]+T[n-1, k-1];
T[_, _] = 0;
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 08 2022 *)
CROSSREFS
First column is A023001, first diagonal is A000537.
Row sums are in A098437.
Replace in recurrence k^3 with k: A008277; with k^2: A008957.
Sequence in context: A156278 A166961 A202988 * A022172 A173005 A015123
KEYWORD
tabl,nonn
AUTHOR
Ralf Stephan, Sep 08 2004
STATUS
approved