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 A137388 Triangle t(n,m)= (m^2-1) * binomial(n,m) * (n+2)/(n+2-m) read by rows, 0<=m<=n. 1
 -1, -1, 0, -1, 0, 6, -1, 0, 15, 20, -1, 0, 27, 64, 45, -1, 0, 42, 140, 175, 84, -1, 0, 60, 256, 450, 384, 140, -1, 0, 81, 420, 945, 1134, 735, 216, -1, 0, 105, 640, 1750, 2688, 2450, 1280, 315, -1, 0, 132, 924, 2970, 5544, 6468, 4752, 2079, 440, -1, 0, 162, 1280, 4725, 10368, 14700, 13824, 8505, 3200, 594 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row sums are -1, -1, 5, 34, 135, 440, 1289, 3530, 9227, 23308, 57357, ... = 3 + n - 2^(n+2) + n^2*2^(n-1) + n*2^n. LINKS FORMULA t(n,m) = (m-1)*(m+1)*binomial(n,m))*binomial(n+2,m)/binomial(n+1,m). EXAMPLE -1; -1, 0; -1, 0, 6; -1, 0, 15, 20; -1, 0, 27, 64, 45; -1, 0, 42, 140, 175, 84; -1, 0, 60, 256, 450, 384, 140; -1, 0, 81, 420, 945, 1134, 735, 216; -1, 0, 105, 640, 1750, 2688, 2450, 1280, 315; -1, 0, 132, 924, 2970, 5544, 6468, 4752, 2079, 440; -1, 0, 162, 1280, 4725, 10368, 14700, 13824, 8505, 3200, 594; MAPLE A137388 := proc(n, m) (m^2-1)*binomial(n, m)*(n+2)/(n+2-m) ; end proc: seq(seq(A137388(n, m), m=0..n), n=0..14) ; # R. J. Mathar, Nov 10 2011 MATHEMATICA a0 = Table[Table[(n - 1)*(n + 1)*Binomial[m, n]*Binomial[m + 2, n]/Binomial[m + 1, n], {n, 0, m}], {m, 0, 10}]; Flatten[a0] CROSSREFS Sequence in context: A204013 A127573 A351110 * A302971 A114153 A119832 Adjacent sequences: A137385 A137386 A137387 * A137389 A137390 A137391 KEYWORD tabl,sign AUTHOR Roger L. Bagula and Gary W. Adamson, Apr 10 2008 STATUS approved

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Last modified March 21 06:13 EDT 2023. Contains 361392 sequences. (Running on oeis4.)