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A177227 Triangle T(n,m) read by rows: equals -binomial(n,m) in general, but 2 if n=m or m=0. 0
2, 2, 2, 2, -2, 2, 2, -3, -3, 2, 2, -4, -6, -4, 2, 2, -5, -10, -10, -5, 2, 2, -6, -15, -20, -15, -6, 2, 2, -7, -21, -35, -35, -21, -7, 2, 2, -8, -28, -56, -70, -56, -28, -8, 2, 2, -9, -36, -84, -126, -126, -84, -36, -9, 2, 2, -10, -45, -120, -210, -252, -210, -120, -45, -10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The row sums are: 2, 4, 2, -2, -10, -26, -58, -122, -250, -506, -1018,... = 6-2^n for n>0. (see A131130).

LINKS

Table of n, a(n) for n=0..64.

FORMULA

T(n,n) = T(n,0)=2. T(n,m) = -binomial(n,m) if 0<m<n.

EXAMPLE

2;

2, 2;

2, -2, 2;

2, -3, -3, 2;

2, -4, -6, -4, 2;

2, -5, -10, -10, -5, 2;

2, -6, -15, -20, -15, -6, 2;

2, -7, -21, -35, -35, -21, -7, 2;

2, -8, -28, -56, -70, -56, -28, -8, 2;

2, -9, -36, -84, -126, -126, -84, -36, -9, 2;

2, -10, -45, -120, -210, -252, -210, -120, -45, -10, 2;

MATHEMATICA

f[t_, n_] := D[t/(1 + t), {t, n}];

a = Table[f[t, n], {n, 0, 20}];

c[t_, n_, m_] = (1/(1 + t))*a[[n + 1]]/(a[[m + 1]]*a[[n - m + 1]]);

Table[Flatten[Table[Table[c[1/q, n, m], {m, 0, n}], {n, 0, 10}]], {q, 2, 10}]

CROSSREFS

Cf. A007318.

Sequence in context: A306240 A109829 A054125 * A174373 A232270 A191517

Adjacent sequences:  A177224 A177225 A177226 * A177228 A177229 A177230

KEYWORD

sign,tabl,easy

AUTHOR

Roger L. Bagula, May 05 2010

STATUS

approved

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Last modified February 17 11:57 EST 2019. Contains 320219 sequences. (Running on oeis4.)