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A176468 A symmetrical triangle:q=3;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, 3, 1, 1, 11, 11, 1, 1, 37, 101, 37, 1, 1, 117, 473, 473, 117, 1, 1, 359, -467, -10331, -467, 359, 1, 1, 1087, -38805, -666047, -666047, -38805, 1087, 1, 1, 3273, -564647, -22609991, -71238207, -22609991, -564647, 3273, 1, 1, 9833, -6313279 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 5, 24, 177, 1182, -10545, -1407528, -117580935, -13535434518,

-2541110736213,...}.

LINKS

Table of n, a(n) for n=0..47.

FORMULA

q=3;

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, 3, 1},

{1, 11, 11, 1},

{1, 37, 101, 37, 1},

{1, 117, 473, 473, 117, 1},

{1, 359, -467, -10331, -467, 359, 1},

{1, 1087, -38805, -666047, -666047, -38805, 1087, 1},

{1, 3273, -564647, -22609991, -71238207, -22609991, -564647, 3273, 1},

{1, 9833, -6313279, -656760847, -6104652967, -6104652967, -656760847, -6313279, 9833, 1},

{1, 29515, -63520279, -18148426855, -499870912759, -1504945075459, -499870912759, -18148426855, -63520279, 29515, 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: A256895 A223256 A013561 * A176421 A168552 A111473

Adjacent sequences:  A176465 A176466 A176467 * A176469 A176470 A176471

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 18 2010

STATUS

approved

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Last modified May 8 15:40 EDT 2021. Contains 343666 sequences. (Running on oeis4.)