The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A145357 Lower triangular array, called S1hat(6), related to partition number array A145356. 5
 1, 6, 1, 42, 6, 1, 336, 78, 6, 1, 3024, 588, 78, 6, 1, 30240, 6804, 804, 78, 6, 1, 332640, 62496, 8316, 804, 78, 6, 1, 3991680, 753984, 85176, 9612, 804, 78, 6, 1, 51891840, 8273664, 1021608, 94248, 9612, 804, 78, 6, 1, 726485760, 109118016, 11394432, 1157688, 102024 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If in the partition array M31hat(6):=A145356 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(6). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039. The first columns are A001725(n+4), A145359, A145360,... LINKS Table of n, a(n) for n=1..50. W. Lang, First 10 rows of the array and more. W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3. FORMULA a(n,m)=sum(product(|S1(6;j,1)|^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S1(6,n,1)|= A049374(n,1) = A001725(n+4) = (n+4)!/5!. EXAMPLE [1];[6,1];[42,6,1];[336,78,6,1];[3024,588,78,6,1];... CROSSREFS A145358(row sums). Sequence in context: A113365 A293172 A145356 * A035529 A135893 A051338 Adjacent sequences: A145354 A145355 A145356 * A145358 A145359 A145360 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang Oct 17 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 19:24 EDT 2024. Contains 372844 sequences. (Running on oeis4.)