The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A174639 A triangular sequence:f(n)=Sum[StirlingS2[n, k], {k, 1, n}];t(n,m)=Binomial[n, m]*f(m + 1)*f(n - m + 1)-Binomial[n,0]*f(1)*f(n+1)+1 0
 1, 1, 1, 1, 4, 1, 1, 16, 16, 1, 1, 69, 99, 69, 1, 1, 318, 548, 548, 318, 1, 1, 1560, 3024, 3624, 3024, 1560, 1, 1, 8139, 17176, 23161, 23161, 17176, 8139, 1, 1, 45094, 101634, 149374, 168134, 149374, 101634, 45094, 1, 1, 264672, 629226, 989046, 1214082 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: 1, 2, 6, 34, 239, 1734, 12794, 96954, 760340, 6194054, 52490379,... LINKS FORMULA f(n)=Sum[StirlingS2[n, k], {k, 1, n}]; t(n,m)=Binomial[n, m]*f(m + 1)*f(n - m + 1)-Binomial[n,0]*f(1)*f(n+1)+1 EXAMPLE {1}, {1, 1}, {1, 4, 1}, {1, 16, 16, 1}, {1, 69, 99, 69, 1}, {1, 318, 548, 548, 318, 1}, {1, 1560, 3024, 3624, 3024, 1560, 1}, {1, 8139, 17176, 23161, 23161, 17176, 8139, 1}, {1, 45094, 101634, 149374, 168134, 149374, 101634, 45094, 1}, {1, 264672, 629226, 989046, 1214082, 1214082, 989046, 629226, 264672, 1}, {1, 1640931, 4079506, 6773431, 8898271, 9706099, 8898271, 6773431, 4079506, 1640931, 1} MATHEMATICA f[n_] := Sum[StirlingS2[n, k], {k, 1, n}]; t[n_, m_] = Binomial[n, m]*f[m + 1]*f[n - m + 1] Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A203846 A118185 A176483 * A173814 A176467 A034802 Adjacent sequences:  A174636 A174637 A174638 * A174640 A174641 A174642 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 25 2010 STATUS approved

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

Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)