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A047265 Triangle a(n,k) (n >= 1, 1<=k<=n) giving coefficient of x^n in expansion of {Product_{j>=1} (1-x^j) - 1 }^k. 1
1, -1, 1, 0, -2, 1, 0, 1, -3, 1, -1, 0, 3, -4, 1, 0, -2, -1, 6, -5, 1, -1, 2, -3, -4, 10, -6, 1, 0, -2, 6, -3, -10, 15, -7, 1, 0, 2, -6, 12, 0, -20, 21, -8, 1, 0, 1, 6, -16, 19, 9, -35, 28, -9, 1, 0, 0, 0, 16, -35, 24, 28, -56, 36, -10, 1, -1, 2, -3, -6, 40 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.

LINKS

Table of n, a(n) for n=1..71.

EXAMPLE

Triangle starts:

   1,

  -1,   1,

   0,  -2,   1,

   0,   1,  -3,   1,

  -1,   0,   3,  -4,   1,

   0,  -2,  -1,   6,  -5,   1,

  -1,   2,  -3,  -4,  10,  -6,   1,

   0,  -2,   6,  -3, -10,  15,  -7,   1,

   0,   2,  -6,  12,   0, -20,  21,  -8,   1,

   0,   1,   6, -16,  19,   9, -35,  28,  -9,   1,

   0,   0,   0,  16, -35,  24,  28, -56,  36, -10,   1,

  -1,   2,  -3,  -6,  40, ...

MATHEMATICA

a[n_, k_] := SeriesCoefficient[(-1)^n*(Product[(1 - x^j), {j, 1, n}] - 1)^k, {x, 0, n}]; Table[a[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Dec 05 2013 *)

PROG

(PARI) a(n, k)=polcoeff((-1)^n*(Ser(prod(i=1, n, 1-x^i)-1)^k), n) \\ Ralf Stephan, Dec 08 2013

CROSSREFS

Columns give A010815, A047654, A047655, A001482-A001488, A047649, A001490, A047938-A047648, A006665.

Sequence in context: A077227 A089263 A156135 * A185962 A279928 A297325

Adjacent sequences:  A047262 A047263 A047264 * A047266 A047267 A047268

KEYWORD

sign,easy,nice,tabl

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)