A241578 Square array read by antidiagonals upwards: 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, 3, 5, 1, 1, 4, 11, 15, 1, 1, 5, 19, 49, 52, 1, 1, 6, 29, 109, 257, 203, 1, 1, 7, 41, 201, 742, 1539, 877, 1, 1, 8, 55, 331, 1657, 5815, 10299, 4140, 1, 1, 9, 71, 505, 3176, 15821, 51193, 75905, 21147, 1, 1, 10, 89, 729, 5497, 35451, 170389, 498118, 609441, 115975, 1

Offset: 0

Author

N. J. A. Sloane, Apr 29 2014

Keywords

• nonn
• tabl

Examples

			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, ...
...
		

Links

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

Crossrefs

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

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

Programs

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: