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 A177851 Triangle read by rows: T(n, m) = binomial(n + m - 3, m - 1)*(2 * m + n - 2) / m, for n>=1 and 1<=m<=n. 0
 1, 2, 2, 3, 5, 7, 4, 9, 16, 25, 5, 14, 30, 55, 91, 6, 20, 50, 105, 196, 336, 7, 27, 77, 182, 378, 714, 1254, 8, 35, 112, 294, 672, 1386, 2640, 4719, 9, 44, 156, 450, 1122, 2508, 5148, 9867, 17875, 10, 54, 210, 660, 1782, 4290, 9438, 19305, 37180, 68068 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This triangle sequence is the number of linearly independent homogeneous harmonic polynomials of degree m in n variables. REFERENCES Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, page 170 LINKS FORMULA Row sums are ((3*n-1)*binomial(2*n-2,n)/(n-1)-1) for n>=2. {1, 4, 15, 54, 195, 713, 2639, 9866, 37179, 140997,...}. EXAMPLE Triangle starts: {1}, {2, 2}, {3, 5, 7}, {4, 9, 16, 25}, {5, 14, 30, 55, 91}, {6, 20, 50, 105, 196, 336}, {7, 27, 77, 182, 378, 714, 1254}, {8, 35, 112, 294, 672, 1386, 2640, 4719}, {9, 44, 156, 450, 1122, 2508, 5148, 9867, 17875}, {10, 54, 210, 660, 1782, 4290, 9438, 19305, 37180, 68068. MAPLE T := (n, m) -> ((2*m + n - 2)/m)*binomial(n + m - 3, m - 1): for n from 1 to 10 do lprint(seq(T(n, k), k=1..n)) od; # Peter Luschny, Dec 16 2015 MATHEMATICA Flatten[Table[Table[((2*m + n - 2)/m)*Binomial[n + m - 3, m - 1], {m, 1, n}], {n, 1, 10}]] CROSSREFS Sequence in context: A139074 A179418 A035428 * A100142 A245935 A178880 Adjacent sequences:  A177848 A177849 A177850 * A177852 A177853 A177854 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, May 14 2010 STATUS approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)