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.

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A226750 Decimal expansion of the number x other than -3 defined by x*e^x = -3/e^3.

Original entry on oeis.org

1, 7, 8, 5, 6, 0, 6, 2, 7, 8, 7, 7, 9, 2, 1, 1, 0, 6, 5, 9, 6, 8, 0, 8, 6, 6, 9, 7, 0, 5, 5, 1, 4, 8, 0, 4, 6, 5, 4, 1, 1, 8, 2, 5, 5, 9, 2, 6, 8, 8, 5, 9, 0, 7, 7, 2, 0, 1, 4, 2, 3, 0, 6, 0, 5, 8, 7, 8, 5, 6, 9, 5, 4, 9, 4, 4, 8, 2, 6, 0, 8, 7, 5, 4, 3, 1, 3, 4, 3, 4, 6, 5, 2, 1, 6, 0, 3, 5, 5, 6, 1, 0, 4, 0, 0
Offset: 0

Views

Author

José María Grau Ribas, Jun 16 2013

Keywords

Examples

			-0.178560627877921106596808669705514804654118255926885907720142306058785...

Links

Crossrefs

Cf. A106533, A217913, A221214, A274712, A274713.

Programs

  • Mathematica
    RealDigits[N[ProductLog[-3/e^3], 105]][[1]]
  • PARI
    solve(x=0,1,3/exp(3)-x*exp(-x)) \\ Charles R Greathouse IV, Nov 19 2013

Extensions

Term a(104) corrected by G. C. Greubel, Nov 16 2017

A274712 a(n) = A008277(3*n-1,n) / (n*(n+1)/2) for n>=1, where A008277 are the Stirling numbers of the second kind.

Original entry on oeis.org

1, 5, 161, 14575, 2671669, 833607138, 397984073059, 270609861663900, 248922595132336125, 298037055910658382175, 450755158919281716609746, 840770855566250627155136090, 1896671776639253430025972662743, 5091278095597325836977485757711800, 16040729445423172146341201903726496024, 58625927208516621021861960954787323034320, 246047331971247756894582227572712664877434765, 1175344062721738572130662103242054758238706829325
Offset: 1

Views

Author

Paul D. Hanna, Jul 03 2016

Keywords

Links

Crossrefs

Cf. A274713.

Programs

  • PARI
    {a(n) = polcoeff( 1/prod(k=1, n, 1-k*x +x*O(x^(2*n))), 2*n-1) / (n*(n+1)/2)}
for(n=1, 20, print1(a(n), ", "))
  • PARI
    {a(n) = abs( stirling(3*n-1, n, 2) / (n*(n+1)/2) )}
for(n=1, 20, print1(a(n), ", "))
  • PARI
    {a(n) = 1/n! * sum(k=0, n, (-1)^(n-k) * binomial(n, k) * k^(3*n-1)) / (n*(n+1)/2)}
for(n=1, 20, print1(a(n), ", "))

Formula

a(n) = A274713(n) / (n*(n+1)/2), where A274713(n) is the number of partitions of a {3*n-1}-set into n nonempty subsets.
a(n) = 1/n! * Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * k^(3*n-1) / (n*(n+1)/2).
a(n) ~ sqrt(2) * 3^(3*n-1) * n^(2*n-7/2) / (exp(2*n) * c^n * (3-c)^(2*n-1) * sqrt(Pi*(1-c))), where c = -LambertW(-3*exp(-3)) = 0.1785606278779211... = -A226750. - Vaclav Kotesovec, Jul 06 2016
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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