A152924 Triangle read by rows: T(n,k) = Stirling2(n, k+1) + abs(Stirling1(n,k)), 0 <= k <= n.

1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 13, 17, 7, 1, 1, 39, 75, 45, 11, 1, 1, 151, 364, 290, 100, 16, 1, 1, 783, 2065, 1974, 875, 196, 22, 1, 1, 5167, 14034, 14833, 7819, 2226, 350, 29, 1, 1, 40575, 112609, 125894, 74235, 25095, 4998, 582, 37, 1, 1, 363391, 1035906, 1206805

Offset

0,5

Links

Table of n, a(n) for n=0..58.

Example

{1},
{1, 1},
{1, 2, 1},
{1, 5, 4, 1},
{1, 13, 17, 7, 1},
{1, 39, 75, 45, 11, 1},
{1, 151, 364, 290, 100, 16, 1},
{1, 783, 2065, 1974, 875, 196, 22, 1},
{1, 5167, 14034, 14833, 7819, 2226, 350, 29, 1},
{1, 40575, 112609, 125894, 74235, 25095, 4998, 582, 37, 1},
{1, 363391, 1035906, 1206805, 766205, 292152, 69153, 10200, 915, 46, 1}

Mathematica

p[x_, n_] = (If[n == 0, 0, Sum[StirlingS2[ n, m]*x^m, {m, 0, n}]/x] + Sum[Abs[StirlingS1[n, m]]*x^m, {m, 0, n}]);
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]

Prog

(PARI) T(n, k) = stirling(n, k+1, 2) + abs(stirling(n, k, 1)) \\ Andrew Howroyd, Jan 09 2024

Crossrefs

Sequence in context: A284949 A263294 A241500 * A220738 A284732 A371766

Adjacent sequences: A152921 A152922 A152923 * A152925 A152926 A152927

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 15 2008

Extensions

Name clarified by Andrew Howroyd, Jan 09 2024

Status

approved