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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
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
Sequence in context: A299019 A347879 A070610 * A104346 A318238 A341075
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 16 2009
STATUS
approved

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Last modified April 20 10:19 EDT 2024. Contains 371814 sequences. (Running on oeis4.)