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 1-4 of 4 results.

A353177 E.g.f. A(x) satisfies A(x) = 1 + (1 - exp(-x)) * A(1 - exp(-x)).

Original entry on oeis.org

1, 1, 1, -2, -13, 61, 612, -8924, -41991, 2821876, -22689807, -1196339088, 45175812442, 10968806278, -63633205318330, 2495113782094766, 31372553334367367, -8832192422722410665, 421480840601004167822, 9536361803340658184343
Offset: 0

Views

Author

Seiichi Manyama, Jun 04 2022

Keywords

Crossrefs

Cf. A135750, A213357, A354574, A354728, A354730.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=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 + x*A(x).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n-k) * k * Stirling2(n,k) * a(k-1).

A355102 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(1 - exp(-x)).

Original entry on oeis.org

1, 2, 8, 36, 112, -500, -10056, 24220, 2184480, -8762868, -1076904200, 13388615108, 954279034416, -32517111227484, -1095519424670888, 104108720480963940, 63376017498217152, -394143964914859213828, 17135457626785509446184, 1359360091138085321022956
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Cf. A354574, A355103.
Cf. A355093.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*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) = 2 * n * Sum_{k=0..n-1} (-1)^(n-k-1) * Stirling2(n-1,k) * a(k).
a(n) = 2 * n * A355093(n-1) for n>0.

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

Cf. A354574, A355102.
Cf. A355094.

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

Cf. A354574, A355102, A355132.

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 1-4 of 4 results.

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

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