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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A032110 "BIJ" (reversible, indistinct, labeled) transform of 0,1,1,1...

Original entry on oeis.org

0, 1, 1, 4, 11, 71, 372, 2850, 21121, 191077, 1793078, 19037624, 214051059, 2628723267, 34285658032, 479609321326, 7104125711717, 111655209047393, 1849927197690186, 32289686161489668
Offset: 1

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Author

Keywords

Formula

(A032032(n) + 1)/2.

A332255 E.g.f.: 1 / (2 - 1 / (2 + x - exp(x))).

Original entry on oeis.org

1, 0, 1, 1, 13, 41, 461, 2745, 32397, 288937, 3794605, 44758649, 665371565, 9660560937, 162652002189, 2782536864697, 52737562595917, 1033546861769513, 21867683869860845, 481630083492884601, 11277805333488014445, 275314710164399079337, 7077059249870048306125
Offset: 0

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Author

Ilya Gutkovskiy, Feb 08 2020

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 22; CoefficientList[Series[1/(2 - 1/(2 + x - Exp[x])), {x, 0, nmax}], x] Range[0, nmax]!
  • PARI
    seq(n)={Vec(serlaplace(1/(2 - 1 / (2 + x - exp(x + O(x*x^n))))))} \\ Andrew Howroyd, Feb 08 2020

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A032032(k) * a(n-k).
a(n) ~ n! * 2^(n-1) / ((c-1) * (2*c-3)^(n+1)), where c = -LambertW(-1, -exp(-3/2)) = 2.3576766739458990584... - Vaclav Kotesovec, Feb 08 2020
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