A225474 Triangle read by rows, k!*2^k*s_2(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0.
1, 1, 2, 3, 8, 8, 15, 46, 72, 48, 105, 352, 688, 768, 384, 945, 3378, 7600, 11040, 9600, 3840, 10395, 39048, 97112, 167040, 193920, 138240, 46080, 135135, 528414, 1418648, 2754192, 3857280, 3736320, 2257920, 645120, 2027025, 8196480, 23393376, 49824768, 79892736
Offset: 0
Examples
[n\k][ 0, 1, 2, 3, 4, 5] [0] 1, [1] 1, 2, [2] 3, 8, 8, [3] 15, 46, 72, 48, [4] 105, 352, 688, 768, 384, [5] 945, 3378, 7600, 11040, 9600, 3840.
Links
- Peter Luschny, Generalized Eulerian polynomials.
- Peter Luschny, The Stirling-Frobenius numbers.
Crossrefs
Programs
-
Mathematica
SFCSO[n_, k_, m_] := SFCSO[n, k, m] = If[k>n || k<0, 0, If[n == 0 && k == 0, 1, m*k*SFCSO[n-1, k-1, m] + (m*n-1)*SFCSO[n-1, k, m]]]; Table[SFCSO[n, k, 2], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 05 2014, translated from Sage *) -
Sage
@CachedFunction def SF_CSO(n, k, m): if k > n or k < 0 : return 0 if n == 0 and k == 0: return 1 return m*k*SF_CSO(n-1, k-1, m) + (m*n-1)*SF_CSO(n-1, k, m) for n in (0..8): [SF_CSO(n, k, 2) for k in (0..n)]
Comments