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.

A330149 Expansion of e.g.f. exp(-x) / (1 + log(1 - x)).

Original entry on oeis.org

1, 0, 2, 7, 47, 368, 3494, 38673, 489341, 6966344, 110199090, 1917589771, 36402276107, 748629861016, 16580304397942, 393443385034069, 9958671117295737, 267824225078212336, 7626444798009902530, 229232204568273395919, 7252798333599466521575, 240948882537990850397536
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 03 2019

Keywords

Comments

Inverse binomial transform of A007840.

Crossrefs

Cf. A052841, A330150.
Cf. A007840, A291979.

Programs

  • Mathematica
    nmax = 21; CoefficientList[Series[Exp[-x]/(1 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * A007840(k).
a(n) ~ n! * exp(n + exp(-1) - 1) / (exp(1) - 1)^(n+1). - Vaclav Kotesovec, Dec 15 2019
a(n) = (-1)^n + Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Dec 19 2023

A368288 Expansion of e.g.f. exp(2*x) / (1 - log(1+x)).

Original entry on oeis.org

1, 3, 9, 28, 92, 326, 1262, 5412, 25720, 136208, 792432, 5105376, 35369072, 271130224, 2163931408, 19516167712, 172444938240, 1853022376064, 16940180000128, 231342744007680, 1864622339520768, 39188769208491520, 160619617213475840, 9585537940543741952, -35595308731629374464
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A006252, A291981, A330150, A368289.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=2^i+sum(j=1, i, (-1)^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

a(n) = 2^n + Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).

A368289 Expansion of e.g.f. exp(-2*x) / (1 - log(1 + x)).

Original entry on oeis.org

1, -1, 1, 0, -4, 22, -98, 508, -2952, 21040, -169360, 1579168, -16208784, 185045936, -2290934384, 30842081632, -445643595776, 6905128910976, -113892295743104, 1995421707848192, -36964967819409152, 722345322667829760, -14842592110869541888
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A006252, A291981, A330150, A368288.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-2)^i+sum(j=1, i, (-1)^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

a(n) = (-2)^n + Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).
Showing 1-3 of 3 results.

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

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