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A178048 Triangle T(n, m) = ( |-A008292(n+1,m+1)^2 + 2*binomial(n, m)^2| + A008292(n+1,m+1)*binomial(n, m) )/2 read by rows. 1
1, 1, 1, 1, 8, 1, 1, 68, 68, 1, 1, 374, 2340, 374, 1, 1, 1742, 47012, 47012, 1742, 1, 1, 7524, 717948, 2942288, 717948, 7524, 1, 1, 31320, 9259560, 122248688, 122248688, 9259560, 31320, 1, 1, 127946, 106900560, 3895086794, 12203119800, 3895086794 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are 1, 2, 10, 138, 3090, 97510, 4393234, 263079138, 20207350402, 1926722077422, 223339810806978, ...

LINKS

Table of n, a(n) for n=0..41.

FORMULA

T(n, m) = T(n,n-m).

EXAMPLE

The triangle starts in row n=0 with columns 0 <= m <= n as

  1;

  1,      1;

  1,      8,         1;

  1,     68,        68,          1;

  1,    374,      2340,        374,           1;

  1,   1742,     47012,      47012,        1742,          1;

  1,   7524,    717948,    2942288,      717948,       7524,         1;

  1,  31320,   9259560,  122248688,   122248688,    9259560,     31320,      1;

  1, 127946, 106900560, 3895086794, 12203119800, 3895086794, 106900560, 127946, 1};

MAPLE

A178048 := proc(n, m) binomial(n, m)*A008292(n+1, m+1)+abs( -A008292(n+1, m+1)^2+2*binomial(n, m)^2) ; %/2; end proc:

seq(seq(A178048(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Nov 26 2010

MATHEMATICA

<< DiscreteMath`Combinatorica`

t[n_, m_] = (Abs[2*Binomial[n, m]^2 - Eulerian[n + 1, m]^2] + Binomial[n, m]*Eulerian[n + 1, m])/2;

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A141686, A008292.

Sequence in context: A203443 A176642 A172346 * A174728 A015121 A156766

Adjacent sequences:  A178045 A178046 A178047 * A178049 A178050 A178051

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, May 18 2010

EXTENSIONS

Definition corrected by R. J. Mathar, Nov 26 2010

STATUS

approved

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Last modified March 2 09:56 EST 2021. Contains 341746 sequences. (Running on oeis4.)