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A174527 Triangle t(n,m) =2*A022167(n,m) - binomial(n, m), 0<=m<=n, read by rows. 1
1, 1, 1, 1, 6, 1, 1, 23, 23, 1, 1, 76, 254, 76, 1, 1, 237, 2410, 2410, 237, 1, 1, 722, 22007, 67740, 22007, 722, 1, 1, 2179, 198905, 1851507, 1851507, 198905, 2179, 1, 1, 6552, 1792492, 50190504, 151826374, 50190504, 1792492, 6552, 1, 1, 19673, 16139204 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are   1, 2, 8, 48, 408, 5296, 113200, 4105184, 255805472, 27442457664, 5089653253824,... = 2*A006117(n)-2^n.

LINKS

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

EXAMPLE

1;

1, 1;

1, 6, 1;

1, 23, 23, 1;

1, 76, 254, 76, 1;

1, 237, 2410, 2410, 237, 1;

1, 722, 22007, 67740, 22007, 722, 1;

1, 2179, 198905, 1851507, 1851507, 198905, 2179, 1;

1, 6552, 1792492, 50190504, 151826374, 50190504, 1792492, 6552, 1;

1, 19673, 16139204, 1356937556, 12348132398, 12348132398, 1356937556, 16139204, 19673, 1},

1, 59038, 145272797, 36653455400, 1001555671874, 3012944335604, 1001555671874, 36653455400, 145272797, 59038, 1;

MAPLE

A174527 := proc(n, k)

        2*A022167(n, k)-binomial(n, k) ;

end proc:

seq(seq(A174527(n, m), m=0..n), n=0..10) ; # R. J. Mathar, Nov 14 2011

MATHEMATICA

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

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

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

CROSSREFS

Cf. A060187

Sequence in context: A152969 A138076 A060187 * A156139 A155863 A173882

Adjacent sequences:  A174524 A174525 A174526 * A174528 A174529 A174530

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Mar 21 2010

STATUS

approved

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Last modified February 24 13:18 EST 2018. Contains 299623 sequences. (Running on oeis4.)