A241579 Square array read by antidiagonals downwards: T(n,k) = Sum_{j=1..k} n^(k-j)*Stirling_2(k,j) (n >= 0, k >= 1).

1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 15, 11, 4, 1, 1, 52, 49, 19, 5, 1, 1, 203, 257, 109, 29, 6, 1, 1, 877, 1539, 742, 201, 41, 7, 1, 1, 4140, 10299, 5815, 1657, 331, 55, 8, 1, 1, 21147, 75905, 51193, 15821, 3176, 505, 71, 9, 1, 1, 115975, 609441, 498118, 170389, 35451, 5497, 729, 89, 10, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

A. Kerber, A matrix of combinatorial numbers related to the symmetric groups, Discrete Math., 21 (1978), 319-321.

A. Kerber, A matrix of combinatorial numbers related to the symmetric groups, Discrete Math., 21 (1978), 319-321. [Annotated scanned copy]

Example

Array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, ...
1, 3, 11, 49, 257, 1539, 10299, 75905, 609441, 5284451, 49134923, 487026929, ...
1, 4, 19, 109, 742, 5815, 51193, 498118, 5296321, 60987817, 754940848, 9983845261, ...
1, 5, 29, 201, 1657, 15821, 170389, 2032785, 26546673, 376085653, 5736591885, 93614616409, ...
1, 6, 41, 331, 3176, 35451, 447981, 6282416, 96546231, 1611270851, 28985293526, 558413253581, ...
1, 7, 55, 505, 5497, 69823, 1007407, 16157905, 284214097, 5432922775, 112034017735, 2476196276617, ...
1, 8, 71, 729, 8842, 125399, 2026249, 36458010, 719866701, 15453821461, 358100141148, 8899677678109, ...
...

Maple

with(combinat):
T:=(n, k)->add(n^(k-j)*stirling2(k, j), j=1..k);
r:=n->[seq(T(n, k), k=1..12)];
for n from 0 to 8 do lprint(r(n)); od:

Crossrefs

Three versions of this array are A111673, A241578, A241579.

Rows and columns give A000110, A004211, A004212, A004213, A005011, A005012, A028387, A241577.

Sequence in context: A078920 A372001 A186020 * A308292 A117396 A125860

Adjacent sequences: A241576 A241577 A241578 * A241580 A241581 A241582

Keyword

nonn,tabl

Author

N. J. A. Sloane, Apr 29 2014

Status

approved