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 1-3 of 3 results.

A293489 E.g.f.: Product_{m>0} (1 + x^(2*m-1) + x^(4*m-2)/2! + x^(6*m-3)/3!).

Original entry on oeis.org

1, 1, 1, 7, 24, 180, 1200, 10080, 97440, 997920, 12096000, 149688000, 2128896000, 31135104000, 515804889600, 8717829120000, 162151621632000, 3092504583168000, 63934815200256000, 1366817864315904000, 31019500604252160000, 733013100880220160000
Offset: 0

Views

Author

Seiichi Manyama, Oct 10 2017

Keywords

Crossrefs

Column k=3 of A293486.
Cf. A293463.

Programs

  • PARI
    N=66; x='x+O('x^N); Vec(serlaplace(prod(m=1, N, 1+x^(2*m-1)+x^(4*m-2)/2+x^(6*m-3)/6)))

A293488 E.g.f.: Product_{m>0} (1 + x^(2*m-1) + x^(4*m-2)/2!).

Original entry on oeis.org

1, 1, 1, 6, 24, 180, 1080, 10080, 90720, 907200, 10886400, 139708800, 2035756800, 29578348800, 479480601600, 7846046208000, 146459529216000, 2845499424768000, 58421660064768000, 1246862279190528000, 28586598596075520000, 664182248232222720000
Offset: 0

Views

Author

Seiichi Manyama, Oct 10 2017

Keywords

Crossrefs

Column k=2 of A293486.

Programs

  • PARI
    N=66; x='x+O('x^N); Vec(serlaplace(prod(m=1, N, 1+x^(2*m-1)+x^(4*m-2)/2)))

Formula

a(n) ~ 2^(-3/4) * c^(1/4) * exp(sqrt(2*c*n) - n) * n^(n-1/4), where c = -polylog(2, -1/2 - I/2) - polylog(2, -1/2 + I/2) = 0.966945612722157030083754546059357521... - Vaclav Kotesovec, Oct 11 2017

A293487 E.g.f.: Product_{m>0} (1 + x^(2*m-1)).

Original entry on oeis.org

1, 1, 0, 6, 24, 120, 720, 5040, 80640, 725760, 7257600, 79833600, 1437004800, 18681062400, 261534873600, 5230697472000, 104613949440000, 1778437140480000, 32011868528640000, 729870602452992000, 17030314057236480000, 408727537373675520000, 8992005822220861440000
Offset: 0

Views

Author

Seiichi Manyama, Oct 10 2017

Keywords

Crossrefs

Column k=1 of A293486.

Programs

  • Mathematica
    nmax = 20; CoefficientList[Series[Product[1 + x^(2*k-1), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 15 2017 *)
  • PARI
    N=66; x='x+O('x^N); Vec(serlaplace(prod(m=1, N, 1+x^(2*m-1))))

Formula

a(n) = n! * A000700(n).
a(n) ~ sqrt(Pi) * exp(Pi*sqrt(n/6) - n) * n^(n - 1/4) / (2^(5/4) * 3^(1/4)). - Vaclav Kotesovec, Oct 15 2017
Showing 1-3 of 3 results.