cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A266944 Expansion of Product_{k>=1} 1 / (1 - 3*x^k)^2.

Original entry on oeis.org

1, 6, 33, 150, 636, 2508, 9501, 34674, 123369, 429396, 1469733, 4959600, 16545597, 54662046, 179124837, 582893052, 1885479918, 6067245570, 19435083054, 62006825166, 197128631562, 624716063502, 1974151076946, 6222482535642, 19567579430643, 61403207075448
Offset: 0

Views

Author

Vaclav Kotesovec, Jan 06 2016

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1-3*x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * n * 3^n, where c = Product_{k>=1} 1/(1-1/3^k)^2 = 1/QPochhammer(1/3)^2 = 3.187340158492291107944103748176139... .

A266945 Expansion of Product_{k>=1} 1 / (1 - 2*x^k)^3.

Original entry on oeis.org

1, 6, 30, 122, 450, 1518, 4830, 14586, 42330, 118622, 322974, 857298, 2226586, 5672046, 14205654, 35040722, 85269114, 204971478, 487307542, 1146995154, 2675265522, 6188176838, 14205568950, 32383725450, 73352114450, 165171276822, 369904716750, 824244212554
Offset: 0

Views

Author

Vaclav Kotesovec, Jan 06 2016

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1-2*x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * n^2 * 2^n, where c = 1/(2*A048651^3) = 1/(2*QPochhammer(1/2)^3) = 20.760229307499152409838537... .
Showing 1-2 of 2 results.