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A176427 A symmetrical triangle sequence:q=2;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q)) 0
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 4, 4, 1, 1, 5, 8, 8, 5, 1, 1, 6, 111, 374, 111, 6, 1, 1, 7, 1041, 8003, 8003, 1041, 7, 1, 1, 8, 6982, 106076, 245384, 106076, 6982, 8, 1, 1, 9, 39030, 1120878, 5309140, 5309140, 1120878, 39030, 9, 1, 1, 10, 195865, 10491942 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 4, 8, 14, 28, 610, 18104, 471518, 12938116, 419594410,...}.

LINKS

Table of n, a(n) for n=0..58.

FORMULA

q=2;

c(n,q)=Product[1 - q^i, {i, 1, n}];

t(n,m,q)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q))

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 3, 3, 1},

{1, 4, 4, 4, 1},

{1, 5, 8, 8, 5, 1},

{1, 6, 111, 374, 111, 6, 1},

{1, 7, 1041, 8003, 8003, 1041, 7, 1},

{1, 8, 6982, 106076, 245384, 106076, 6982, 8, 1},

{1, 9, 39030, 1120878, 5309140, 5309140, 1120878, 39030, 9, 1},

{1, 10, 195865, 10491942, 97749860, 202719054, 97749860, 10491942, 195865, 10, 1}

MATHEMATICA

<< DiscreteMath`Combinatorica` ;

c[n_, q_] = Product[1 - q^i, {i, 1, n}];

t[n_, m_, q_] = -Eulerian[n + 1, m] + 2*c[n, q]/(c[m, q]*c[n - m, q]);

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

CROSSREFS

Sequence in context: A318274 A049695 A096589 * A099573 A107430 A255741

Adjacent sequences:  A176424 A176425 A176426 * A176428 A176429 A176430

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 17 2010

STATUS

approved

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Last modified November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)