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A174948 A symmetrical triangle sequence based on:q=1/12;t(n,m,q)=12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/((n + 1)!* m!)) + ((2*n - m + 1)!/((n + 1)!*(n - m)!)))*q) 0
1, 1, 1, 1, 9, 1, 1, 7, 7, 1, 1, -31, -29, -31, 1, 1, -201, -251, -251, -201, 1, 1, -861, -1196, -1267, -1196, -861, 1, 1, -3357, -4883, -5401, -5401, -4883, -3357, 1, 1, -12783, -18953, -21483, -22121, -21483, -18953, -12783, 1, 1, -48521, -72479 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 11, 16, -89, -902, -5379, -27280, -128557, -582338, -2575441,...}

LINKS

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

FORMULA

q=1/12;

t(n,m,q)=12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/((n + 1)!* m!)) + ((2*n - m + 1)!/((n + 1)!*(n - m)!)))*q);

out_n,m,q=t(n,m,q)-t(n,0,q)+1

EXAMPLE

{1},

{1, 1},

{1, 9, 1},

{1, 7, 7, 1},

{1, -31, -29, -31, 1},

{1, -201, -251, -251, -201, 1},

{1, -861, -1196, -1267, -1196, -861, 1},

{1, -3357, -4883, -5401, -5401, -4883, -3357, 1},

{1, -12783, -18953, -21483, -22121, -21483, -18953, -12783, 1},

{1, -48521, -72479, -83171, -86999, -86999, -83171, -72479, -48521, 1},

{1, -184645, -276572, -319219, -336676, -341219, -336676, -319219, -276572, -184645, 1}

MATHEMATICA

t[n_, m_, q_] = 12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/((n + 1)!* m!)) + ((2*n - m + 1)!/((n + 1)!*(n - m)!)))*q);

Table[Flatten[Table[Table[t[ n, m, q] - t[n, 0, q] + 1, {m, 0, n}], {n, 0, 10}]], {q, 0, 1, 1/12}]

CROSSREFS

Sequence in context: A203141 A085660 A195703 * A092578 A331247 A128060

Adjacent sequences:  A174945 A174946 A174947 * A174949 A174950 A174951

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 02 2010

STATUS

approved

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Last modified October 26 02:14 EDT 2021. Contains 348256 sequences. (Running on oeis4.)