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 A176487 Triangle t(n,m) = binomial(n,m) + A008292(n+1,m+1)-1 read by rows. 6
 1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 29, 71, 29, 1, 1, 61, 311, 311, 61, 1, 1, 125, 1205, 2435, 1205, 125, 1, 1, 253, 4313, 15653, 15653, 4313, 253, 1, 1, 509, 14635, 88289, 156259, 88289, 14635, 509, 1, 1, 1021, 47875, 455275, 1310479, 1310479, 455275, 47875 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are 1, 2, 7, 28, 131, 746, 5097, 40440, 363127, 3629302, 39917813,.. = 2^n-n+A033312(n+1). LINKS FORMULA t(n,m) = A007318(n,m)+A008292(n+1,m+1)-1 , 0<=m<=n. t(n,m) = 2*A141689(n+1,m+1)-1. - R. J. Mathar, Jan 19 2011 EXAMPLE 1; 1, 1; 1, 5, 1; 1, 13, 13, 1; 1, 29, 71, 29, 1; 1, 61, 311, 311, 61, 1; 1, 125, 1205, 2435, 1205, 125, 1; 1, 253, 4313, 15653, 15653, 4313, 253, 1; 1, 509, 14635, 88289, 156259, 88289, 14635, 509, 1; 1, 1021, 47875, 455275, 1310479, 1310479, 455275, 47875, 1021, 1; 1, 2045, 152681, 2203607, 9738323, 15724499, 9738323, 2203607, 152681, 2045, 1; MAPLE A176487 := proc(n, k)     binomial(n, k)+A008292(n+1, k+1)-1 ; end proc: # R. J. Mathar, Jun 16 2015 MATHEMATICA << DiscreteMath`Combinatorica`; t[n_, m_, 0] := Binomial[n, m]; t[n_, m_, 1] := Eulerian[1 + n, m]; t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 1] + t[n, m, q - 2] - 1; Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}] CROSSREFS Cf. A007318, A008292 Sequence in context: A324009 A143007 A152654 * A272644 A157177 A298240 Adjacent sequences:  A176484 A176485 A176486 * A176488 A176489 A176490 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Apr 19 2010 STATUS approved

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Last modified June 6 03:48 EDT 2020. Contains 334858 sequences. (Running on oeis4.)