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.

Previous Showing 51-53 of 53 results.

A332256 E.g.f.: 1 / (2 - exp(sinh(x))).

Original entry on oeis.org

1, 1, 3, 14, 87, 672, 6231, 67412, 833475, 11593140, 179170947, 3045978388, 56490392943, 1134970258372, 24557211519951, 569294311105300, 14077429483372251, 369861235318338404, 10289111057247180411, 302132879478864660340, 9338874072977661538119
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 08 2020

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 20; CoefficientList[Series[1/(2 - Exp[Sinh[x]]), {x, 0, nmax}], x] Range[0, nmax]!
  • PARI
    seq(n)={Vec(serlaplace(1/(2 - exp(sinh(x + O(x*x^n))))))} \\ Andrew Howroyd, Feb 08 2020

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A003724(k) * a(n-k).
a(n) ~ n! / (2 * sqrt(1 + log(2)^2) * (log(log(2) + sqrt(1 + log(2)^2)))^(n+1)). - Vaclav Kotesovec, Feb 08 2020

A346749 E.g.f.: exp( (x * (1 + x) * exp(x) - sinh(x)) / 4 ).

Original entry on oeis.org

1, 0, 1, 2, 7, 26, 124, 628, 3565, 22096, 149176, 1080868, 8372543, 68957268, 601351748, 5528967282, 53416626441, 540682811424, 5718911631856, 63060992662328, 723382253378395, 8616075340134868, 106374847828850676, 1359171823319541070, 17946987240664242493
Offset: 0

Views

Author

Ilya Gutkovskiy, Aug 01 2021

Keywords

Comments

Exponential transform of A002620.

Crossrefs

Programs

  • Mathematica
    nmax = 24; CoefficientList[Series[Exp[(x (1 + x) Exp[x] - Sinh[x])/4], {x, 0, nmax}], x] Range[0, nmax]!
    a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Floor[k^2/4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002620(k) * a(n-k).

A372508 Expansion of e.g.f. exp(sinh(x)) - exp(cosh(x) - 1).

Original entry on oeis.org

0, 1, 0, 2, 1, 12, 6, 128, 78, 1872, 1613, 37600, 38336, 990784, 1124280, 32333824, 41622181, 1272660224, 1843050734, 59527313920, 94591980910, 3252626013184, 5602035320753, 204354574172160, 380190518533920, 14594815769038848, 29179899891380592, 1174376539738169344
Offset: 0

Views

Author

Ilya Gutkovskiy, May 04 2024

Keywords

Comments

Number of partitions of n-set into odd blocks minus number of partitions of n-set into even blocks.

Crossrefs

Programs

  • Mathematica
    nmax = 27; CoefficientList[Series[Exp[Sinh[x]] - Exp[Cosh[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
Previous Showing 51-53 of 53 results.