A298986 -id:A298986 - cp's OEIS frontend

A298985 a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^k)^k.

1, 1, 8, 54, 496, 5400, 73728, 1204322, 23167808, 512093178, 12781430600, 355128859129, 10863077554224, 362572265689777, 13107541496092960, 510105773344747725, 21258690342206888192, 944467894258279964254, 44555341678790400325512, 2224158766859058600584834, 117123916650423288611260400

Offset: 0

Ilya Gutkovskiy, Jan 31 2018

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..380

Cf. A000219, A124577, A261561, A261565, A266941, A297329, A298986, A298987, A298988.

b:= proc(n, i, k) option remember;   `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(i+j-1, j)*b(n-i*j, i-1, k)*k^j, j=0..n/i)))
    end:
a:= n-> b(n$3):
seq(a(n), n=0..30);  # Alois P. Heinz, Sep 23 2018

Table[SeriesCoefficient[Product[1/(1 - n x^k)^k, {k, 1, n}], {x, 0, n}], {n, 0, 20}]

a(n) ~ n^n. - Vaclav Kotesovec, Feb 02 2018

A298987 a(n) = [x^n] Product_{k>=1} (1 + n*x^k)^k.

Original entry on oeis.org

1, 1, 4, 27, 80, 400, 1908, 6223, 31296, 116478, 450100, 1828915, 7360848, 26906828, 95776772, 403908975, 1421758720, 5072014447, 18481180644, 68350964211, 246180936400, 827642046294, 2958748580084, 10294629775620, 36607347335232, 120800714172500, 407951731319860, 1405943613730899

Offset: 0

Ilya Gutkovskiy, Jan 31 2018

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Cf. A026007, A261562, A266857, A266891, A291698, A297322, A298985, A298986, A298988.

Table[SeriesCoefficient[Product[(1 + n x^k)^k, {k, 1, n}], {x, 0, n}], {n, 0, 27}]

A298988 a(n) = [x^n] Product_{k>=1} 1/(1 + n*x^k)^k.

Original entry on oeis.org

1, -1, 0, -18, 208, -2400, 36504, -663754, 13808320, -324176418, 8487126400, -245122390601, 7741417124880, -265402847130421, 9816338228638872, -389618889514254225, 16518399076342421248, -745025763154442071130, 35619835529954597786208, -1799459812004380374518790, 95780758238408017088795600

Offset: 0

Ilya Gutkovskiy, Jan 31 2018

sign

Cf. A255528, A261566, A261567, A266971, A292134, A297326, A298985, A298986, A298987.

Table[SeriesCoefficient[Product[1/(1 + n x^k)^k, {k, 1, n}], {x, 0, n}], {n, 0, 20}]

a(n) ~ (-1)^n * n^n * (1 - 2/n + 6/n^2 - 14/n^3 + 33/n^4 - 70/n^5 + 149/n^6 - 298/n^7 + 591/n^8 - 1132/n^9 + 2139/n^10 + ...), for coefficients, see A005380. - Vaclav Kotesovec, Aug 21 2018

cp's OEIS Frontend

A298985 a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^k)^k.

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A298987 a(n) = [x^n] Product_{k>=1} (1 + n*x^k)^k.

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Links

Crossrefs

Programs

Mathematica

A298988 a(n) = [x^n] Product_{k>=1} 1/(1 + n*x^k)^k.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula