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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

Table of n, a(n) for n=0..52.

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: A114123 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 February 17 02:33 EST 2019. Contains 320200 sequences. (Running on oeis4.)