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.

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

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.

A355207 E.g.f. A(x) satisfies A'(x) = 1 + 2 * A(1 - exp(-x)).

Original entry on oeis.org

1, 2, 2, -6, -10, 142, -434, -4478, 88122, -688518, -4032346, 268040678, -5689167298, 53999999466, 1413830543394, -98561802143670, 3282601333608550, -59117973090349066, -1121454296035526786, 171971593399059103618, -10034063428244586340158
Offset: 1

Views

Author

Seiichi Manyama, Jun 24 2022

Keywords

Crossrefs

Programs

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

Formula

a(1) = 1; a(n+1) = 2 * Sum_{k=1..n} (-1)^(n-k) * Stirling2(n,k) * a(k).

A355094 E.g.f. A(x) satisfies A(x) = 1 + 3 * (1 - exp(-x)) * A(1 - exp(-x)).

Original entry on oeis.org

1, 3, 15, 84, 321, -2157, -57126, -23496, 19229199, 114026754, -14369595177, -124727102772, 21679898019936, 89714147328354, -57010454409251982, 653678598376462566, 223463102168891738085, -9691395708350731626375, -1087655068021435814109648
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*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 + 3*x*A(x).
a(0) = 1; a(n) = 3 * Sum_{k=1..n} (-1)^(n-k) * k * Stirling2(n,k) * a(k-1).

A355123 E.g.f. A(x) satisfies A(x) = 1 + (1 - exp(-x)) * A(2 * (1 - exp(-x))).

Original entry on oeis.org

1, 1, 3, 25, 611, 41721, 7326115, 3120454233, 3105527125475, 7041597540281017, 35733375744777784867, 400526056950063657595929, 9816824637930442994222501475, 521959475771315485798501882623609, 59814953381855591853355367174623538851
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]=sum(j=1, i, (-1)^(i-j)*j*2^(j-1)*stirling(i, j, 2)*v[j])); v;

Formula

E.g.f. A(x) satisfies: A(-log(1-x)) = 1 + x*A(2*x).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n-k) * k * 2^(k-1) * Stirling2(n,k) * a(k-1).
Showing 1-4 of 4 results.