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 1-6 of 6 results.

A354729 E.g.f. A(x) satisfies A(x) = 1 + x * A(log(1+x)).

Original entry on oeis.org

1, 1, 2, 3, -4, -30, 234, 679, -35848, 305208, 6762360, -290545486, 2866197828, 186075548048, -10575881477630, 151622861284395, 14937532353298992, -1269964031741331704, 32904195657758601624, 2814524425307181390432, -395787864674458924551840
Offset: 0

Views

Author

Seiichi Manyama, Jun 04 2022

Keywords

Crossrefs

Cf. A048801, A354728, A354730.

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, stirling(i-1, j, 1)*v[j+1])); v;

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} Stirling1(n-1,k) * a(k).
a(n) = n * A354728(n-1) for n>0.

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).

A354574 E.g.f. A(x) satisfies A(x) = 1 + x * A(1 - exp(-x)).

Original entry on oeis.org

1, 1, 2, 3, -8, -65, 366, 4284, -71392, -377919, 28218760, -249587877, -14356069056, 587285561746, 153563287892, -954498079774950, 39921820513516256, 533333406684245239, -158979463609003391970, 8008135971419079188618, 190727236066813163686860
Offset: 0

Views

Author

Seiichi Manyama, Jun 04 2022

Keywords

Crossrefs

Cf. A048801, A353177, A354729, A354730.

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)*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) * Stirling2(n-1,k) * a(k).
a(n) = n * A353177(n-1) for n>0.

A355106 E.g.f. A(x) satisfies: A(x) = 1 + 2 * x * A(-log(1-x)).

Original entry on oeis.org

1, 2, 8, 60, 704, 11640, 254736, 7071512, 241414400, 9898632864, 478455967200, 26853032524912, 1728192188667072, 126200480666269984, 10363161616018802080, 949530356895864383280, 96418968027002031636480, 10785892383962319840160640
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Cf. A354730, A355107.
Cf. A355098.

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, abs(stirling(i-1, j, 1))*v[j+1])); v;

Formula

a(0) = 1; a(n) = 2 * n * Sum_{k=0..n-1} |Stirling1(n-1,k)| * a(k).
a(n) = 2 * n * A355098(n-1) for n>0.

A355107 E.g.f. A(x) satisfies: A(x) = 1 + 3 * x * A(-log(1-x)).

Original entry on oeis.org

1, 3, 18, 189, 2988, 65070, 1845666, 65593773, 2838648888, 146342004696, 8832171768840, 615243982098438, 48886929048261636, 4387169287407671856, 440884788552635315490, 49250783623005351369405, 6076420246639538049330288, 823299493223605468234344696
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Cf. A354730, A355106.
Cf. A355099.

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, abs(stirling(i-1, j, 1))*v[j+1])); v;

Formula

a(0) = 1; a(n) = 3 * n * Sum_{k=0..n-1} |Stirling1(n-1,k)| * a(k).
a(n) = 3 * n * A355099(n-1) for n>0.

A355126 E.g.f. A(x) satisfies: A(x) = 1 + x * A(-2 * log(1-x)).

Original entry on oeis.org

1, 1, 4, 54, 1936, 168780, 34360128, 15979581632, 16740281020160, 39091514910283872, 201702609432140369280, 2281926772696486970224192, 56217269029941735581289119232, 2997472083791372184890466743907712, 344025706673467887482938899075885442048
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2022

Keywords

Crossrefs

Cf. A354730, A355106, A355134.

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, 2^j*abs(stirling(i-1, j, 1))*v[j+1])); v;

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} 2^k * |Stirling1(n-1,k)| * a(k).
a(n) = n * A355134(n-1) for n>0.
Showing 1-6 of 6 results.

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

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