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.

A354728 E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(log(1+x)).

Original entry on oeis.org

1, 1, 1, -1, -6, 39, 97, -4481, 33912, 676236, -26413226, 238849819, 14313503696, -755420105545, 10108190752293, 933595772081187, -74703766573019512, 1828010869875477868, 148132864489851652128, -19789393233722946227592, 910780967051245532791008
Offset: 0

Views

Author

Seiichi Manyama, Jun 04 2022

Keywords

Crossrefs

Cf. A135750, A213357, A354729.

Programs

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

Formula

E.g.f. A(x) satisfies: A(exp(x) - 1) = 1 + x*A(x).
a(0) = 1; a(n) = Sum_{k=1..n} k * Stirling1(n,k) * a(k-1).

A354730 E.g.f. A(x) satisfies: A(x) = 1 + x * A(-log(1-x)).

Original entry on oeis.org

1, 1, 2, 9, 68, 750, 11214, 216559, 5217176, 152742528, 5324034480, 217322508194, 10248159667140, 551968543756448, 33627829222316770, 2298114390067518705, 174893648144384932176, 14727538317383970615352, 1364522959678851181512504
Offset: 0

Views

Author

Seiichi Manyama, Jun 04 2022

Keywords

Crossrefs

Cf. A048801, A135750, A354729.

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, abs(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 * A135750(n-1) for n>0.

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.

A355104 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(log(1+x)).

Original entry on oeis.org

1, 2, 8, 36, 128, -120, -5904, 8792, 1015808, -7346016, -403678560, 9772765552, 226781102016, -17673167204576, 72041280334240, 38308664521315920, -1705420687695700992, -64315848872486436736, 11313330167773175073408, -326450445457848188386944
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Cf. A354729, A355105.
Cf. A355096.

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, 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 * A355096(n-1) for n>0.

A355105 E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(log(1+x)).

Original entry on oeis.org

1, 3, 18, 135, 1044, 6210, -5994, -760347, -3009960, 261689616, 1960394400, -220644396522, -1043258760828, 366570209524896, -3109452797977470, -972076070389224105, 36160406771040130320, 3274635904971823559880, -331428842765036684941320
Offset: 0

Views

Author

Seiichi Manyama, Jun 19 2022

Keywords

Crossrefs

Cf. A354729, A355104.
Cf. A355097.

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, 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 * A355097(n-1) for n>0.

A355124 E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * log(1+x)).

Original entry on oeis.org

1, 1, 4, 42, 1168, 84180, 15107328, 6495857312, 6492989426432, 14753072834027424, 74941835564789489280, 840421638561217307501632, 20603672787268830442103493120, 1095629510349075557617215030858112, 125563465926494619940863277689861766144
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2022

Keywords

Crossrefs

Cf. A354729, A355104, A355133.

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*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 * A355133(n-1) for n>0.
Showing 1-6 of 6 results.

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