The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A156820 T(n,m) = Sum_{j=0..m} (-1)^(j + m)*(j + 1)^n*binomial(m, j) + Sum_{j=0..(n-m)} (-1)^(j - m + n )*(1 + j)^n*binomial(n-m, j). 0
 2, 2, 2, 3, 6, 3, 7, 19, 19, 7, 25, 75, 100, 75, 25, 121, 391, 570, 570, 391, 121, 721, 2583, 3962, 4200, 3962, 2583, 721, 5041, 20287, 33852, 35406, 35406, 33852, 20287, 5041, 40321, 181695, 338690, 364140, 333648, 364140, 338690, 181695, 40321, 362881 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are 2, 4, 12, 52, 300, 2164, 18732, 189172, 2183340, 28349044, ... = 2 * A000629. LINKS Table of n, a(n) for n=0..45. FORMULA T(n,m) = Sum_{j=0..m}[(-1)^(j + m)*(j + 1)^n*binomial(m, j)] + Sum_{j=0..(n-m)}[(-1)^(j - m + n )*(1 + j)^n*binomial(n-m, j)]. Apparently, T = A007318 * A131689 + A123125 * A007318 = A028246 + row reversed A028246. - Tom Copeland, Jan 26 2015 EXAMPLE Triangle begins: 2 2, 2 3, 6, 3 7, 19, 19, 7 25, 75, 100, 75, 25 121, 391, 570, 570, 391, 121 721, 2583, 3962, 4200, 3962, 2583, 721 5041, 20287, 33852, 35406, 35406, 33852, 20287, 5041 40321, 181695, 338690, 364140, 333648, 364140, 338690, 181695, 40321 MATHEMATICA w[n_, m_] = Sum[(-1)^(j + m)*(j + 1)^n*Binomial[m, j], {j, 0, m}] + Sum[(-1)^( j - m + n )*(1 + j)^n Binomial[ -m + n, j], {j, 0, n - m}]; Table[Table[w[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Cf. A000629, A028246, A131689, A123125, A007318. Sequence in context: A299019 A347879 A070610 * A104346 A318238 A341075 Adjacent sequences: A156817 A156818 A156819 * A156821 A156822 A156823 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 16 2009 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 April 20 10:19 EDT 2024. Contains 371814 sequences. (Running on oeis4.)