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A302056 Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1 - x^j)^4 is zero. 7
9, 14, 19, 24, 31, 34, 39, 42, 44, 49, 53, 59, 64, 65, 69, 74, 75, 82, 84, 86, 89, 94, 97, 99, 108, 109, 111, 114, 116, 119, 124, 130, 133, 134, 139, 144, 149, 150, 152, 157, 159, 163, 164, 167, 169, 174, 180, 184, 185, 189, 194, 196, 198, 199, 201, 203, 207, 209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers k such that number of partitions of k into an even number of distinct parts equals number of partitions of k into an odd number of distinct parts, with 4 types of each part.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Index entries for expansions of Product_{k >= 1} (1-x^k)^m

MATHEMATICA

Flatten[Position[nmax = 210; Rest[CoefficientList[Series[QPochhammer[x]^4, {x, 0, nmax}], x]], 0]]

Flatten[Position[nmax = 210; Rest[CoefficientList[Series[Sum[(-1)^j x^(j (3 j + 1)/2), {j, -nmax, nmax}]^4, {x, 0, nmax}], x]], 0]]

Flatten[Position[nmax = 210; Rest[CoefficientList[Series[Exp[-4 Sum[DivisorSigma[1, j] x^j/j, {j, 1, nmax}]], {x, 0, nmax}], x]], 0]]

PROG

(PARI) x='x+O('x^999); v=Vec(eta(x)^4 - 1); for(k=1, #v, if(v[k]==0, print1(k, ", "))); \\ Altug Alkan, Mar 31 2018, after Joerg Arndt at A213250

CROSSREFS

Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1 - x^j)^m is zero: A090864 (m = 1), A213250 (m = 2), A014132 (m = 3), this sequence (m = 4), A302057 (m = 5), A020757 (m = 6).

Cf. A000727.

Sequence in context: A244466 A171123 A327896 * A173792 A034703 A006624

Adjacent sequences:  A302053 A302054 A302055 * A302057 A302058 A302059

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 31 2018

STATUS

approved

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Last modified February 27 12:47 EST 2020. Contains 332306 sequences. (Running on oeis4.)