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.

A355093 E.g.f. A(x) satisfies A(x) = 1 + 2 * (1 - exp(-x)) * A(1 - exp(-x)).

Original entry on oeis.org

1, 2, 6, 14, -50, -838, 1730, 136530, -486826, -53845210, 608573414, 39761626434, -1250658124134, -39125693738246, 3470290682698798, 1980500546819286, -11592469556319388642, 475984934077375262394, 35772633977318034763762
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies: A(-log(1-x)) = 1 + 2*x*A(x).
a(0) = 1; a(n) = 2 * Sum_{k=1..n} (-1)^(n-k) * k * Stirling2(n,k) * a(k-1).

A355103 E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(1 - exp(-x)).

Original entry on oeis.org

1, 3, 18, 135, 1008, 4815, -38826, -1199646, -563904, 519188373, 3420802620, -474196640841, -4490175699792, 845516022777504, 3767994187790868, -2565470448416339190, 31376572722070203168, 11396618210613478642335, -523335368250939507824250
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*i*sum(j=0, i-1, (-1)^(i-j-1)*stirling(i-1, j, 2)*v[j+1])); v;

Formula

a(0) = 1; a(n) = 3 * n * Sum_{k=0..n-1} (-1)^(n-k-1) * Stirling2(n-1,k) * a(k).
a(n) = 3 * n * A355094(n-1) for n>0.

A355130 E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * (1 - exp(-x))).

Original entry on oeis.org

1, 1, 4, 42, 1160, 83270, 14923212, 6414048354, 6410464368912, 14565079937500542, 73986188807621474900, 829702542906852010728090, 20340869993779258576653846936, 1081654382501102944417336793863094, 123961854316018592747078219803021082332
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2022

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} (-1)^(n-k-1) * 2^k * Stirling2(n-1,k) * a(k).
a(n) = n * A355132(n-1) for n>0.
Showing 1-3 of 3 results.