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A176467 A symmetrical triangle:q=2;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=A060187(n,m)-c(n,q)/(c(m,q)*c(n-m,q))+1 0
1, 1, 1, 1, 4, 1, 1, 17, 17, 1, 1, 62, 196, 62, 1, 1, 207, 1528, 1528, 207, 1, 1, 660, 9893, 22154, 9893, 660, 1, 1, 2053, 57991, 247913, 247913, 57991, 2053, 1, 1, 6298, 320818, 2388134, 4474228, 2388134, 320818, 6298, 1, 1, 19163, 1712906, 20919938 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 6, 36, 322, 3472, 43262, 615916, 9904730, 177511112, 3486135606,...}.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

q=2;

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

t(n,m,q)=A060187(n,m)-c(n,q)/(c(m,q)*c(n-m,q))+1

EXAMPLE

{1},

{1, 1},

{1, 4, 1},

{1, 17, 17, 1},

{1, 62, 196, 62, 1},

{1, 207, 1528, 1528, 207, 1},

{1, 660, 9893, 22154, 9893, 660, 1},

{1, 2053, 57991, 247913, 247913, 57991, 2053, 1},

{1, 6298, 320818, 2388134, 4474228, 2388134, 320818, 6298, 1},

{1, 19163, 1712906, 20919938, 66103548, 66103548, 20919938, 1712906, 19163, 1},

{1, 58016, 8941891, 171953190, 853179296, 1417870818, 853179296, 171953190, 8941891, 58016, 1}

MATHEMATICA

(*A060187*);

p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];

f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];

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

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

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

CROSSREFS

Cf. A060187

Sequence in context: A176483 A174639 A173814 * A034802 A177262 A203092

Adjacent sequences:  A176464 A176465 A176466 * A176468 A176469 A176470

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 18 2010

STATUS

approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)