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.

A352659 a(n) = n! * Sum_{k=0..floor(n/3)} 1 / (3*k)!.

Original entry on oeis.org

1, 1, 2, 7, 28, 140, 841, 5887, 47096, 423865, 4238650, 46625150, 559501801, 7273523413, 101829327782, 1527439916731, 24439038667696, 415463657350832, 7478345832314977, 142088570813984563, 2841771416279691260, 59677199741873516461, 1312898394321217362142
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 25 2022

Keywords

Crossrefs

Programs

  • Mathematica
    Table[n! Sum[1/(3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]
    nmax = 22; CoefficientList[Series[(Exp[x] + 2 Exp[-x/2] Cos[Sqrt[3] x/2])/(3 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!
  • PARI
    a(n) = n! * sum(k=0, n\3, 1/(3*k)!); \\ Michel Marcus, Mar 29 2022

Formula

E.g.f.: (exp(x) + 2 * exp(-x/2) * cos(sqrt(3)*x/2)) / (3*(1 - x)).
a(n) = floor(c * n!), where c = 1.16805831... = A143819.

A349087 a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k / (4*k)!.

Original entry on oeis.org

1, 1, 2, 6, 23, 115, 690, 4830, 38641, 347769, 3477690, 38254590, 459055079, 5967716027, 83548024378, 1253220365670, 20051525850721, 340875939462257, 6135766910320626, 116579571296091894, 2331591425921837879, 48963419944358595459, 1077195238775889100098
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 25 2022

Keywords

Crossrefs

Programs

  • Mathematica
    Table[n! Sum[(-1)^k/(4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]
    nmax = 22; CoefficientList[Series[Cos[x/Sqrt[2]] Cosh[x/Sqrt[2]]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: cos(x/sqrt(2)) * cosh(x/sqrt(2)) / (1 - x).
a(n) = round(c * n!), where c = 0.9583581... = A346440.

A349089 a(n) = n! * Sum_{k=0..floor((n-1)/4)} 1 / (4*k+1)!.

Original entry on oeis.org

0, 1, 2, 6, 24, 121, 726, 5082, 40656, 365905, 3659050, 40249550, 482994600, 6278929801, 87905017214, 1318575258210, 21097204131360, 358652470233121, 6455744464196178, 122659144819727382, 2453182896394547640, 51516840824285500441, 1133370498134281009702
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 25 2022

Keywords

Crossrefs

Programs

  • Mathematica
    Table[n! Sum[1/(4 k + 1)!, {k, 0, Floor[(n - 1)/4]}], {n, 0, 22}]
    nmax = 22; CoefficientList[Series[(Sin[x] + Sinh[x])/(2 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: (sin(x) + sinh(x)) / (2*(1 - x)).
a(n) = floor(c * n!) for n > 0, where c = 1.008336089... = A334363.
Showing 1-3 of 3 results.