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 1-5 of 5 results.

A355087 E.g.f. A(x) satisfies A(x) = 1 - log(1-x) * A(3*x).

Original entry on oeis.org

1, 1, 7, 200, 22008, 8968614, 13103201154, 66911528280456, 1170951806182816008, 69148802888161984160496, 13610904625275511792310726256, 8840888240006182011615570947541552, 18793694994107665289261434484161549856688
Offset: 0

Views

Author

Seiichi Manyama, Jun 18 2022

Keywords

Crossrefs

Cf. A007840, A355086.
Cf. A355088.

Programs

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} 3^(n-k) * (k-1)! * binomial(n,k) * a(n-k).

A355230 E.g.f. A(x) satisfies A'(x) = 1 - log(1-x) * A(2*x).

Original entry on oeis.org

0, 1, 0, 4, 6, 144, 860, 30656, 497168, 33543808, 1300171872, 178516634624, 15640422963968, 4483114311886336, 862178272953520640, 520264199498699214848, 215806526739662643193856, 274505260166616222726586368
Offset: 0

Views

Author

Seiichi Manyama, Jun 25 2022

Keywords

Crossrefs

Cf. A355086, A355229, A355231.

Programs

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

Formula

a(0) = 0, a(1) = 1; a(n+1) = Sum_{k=1..n-1} 2^(n-k) * (k-1)! * binomial(n,k) * a(n-k).

A355084 E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(2*x).

Original entry on oeis.org

1, 1, 3, 32, 962, 74604, 14102416, 6268777248, 6394217598800, 14703540690658848, 75208658403123879744, 846736815151560907880448, 20804324374762392749905814784, 1107653447201119751335031683041792, 127026805293926861783650032004892737536
Offset: 0

Views

Author

Seiichi Manyama, Jun 18 2022

Keywords

Crossrefs

Cf. A006252, A355085.
Cf. A352860, A355086.

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)^(j-1)*2^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * 2^(n-k) * (k-1)! * binomial(n,k) * a(n-k).

A355121 E.g.f. A(x) satisfies A(x) = 1 - log(1-x) * A(-2 * log(1-x)).

Original entry on oeis.org

1, 1, 5, 74, 2778, 248244, 51212444, 23984832416, 25218677193200, 59000757443457072, 304720138059811544048, 3449059394896458379058208, 84991203371449537414272981856, 4532232538284485346856696552505728, 520204832574009673696495358635072488576
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2022

Keywords

Crossrefs

Cf. A135750, A355086, A355098.

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

Formula

E.g.f. A(x) satisfies: A(1 - exp(-x)) = 1 + x*A(2*x).
a(0) = 1; a(n) = Sum_{k=1..n} k * 2^(k-1) * |Stirling1(n,k)| * a(k-1).

A367828 E.g.f. A(x) satisfies A(x) = (1 - log(1 - x) * A(2*x)) / (1 - x).

Original entry on oeis.org

1, 2, 13, 209, 7874, 687194, 138026428, 63273019396, 65547617642192, 151904702763916944, 780028188748068778464, 8799101018162158392857376, 216405047530763040469557821568, 11527355297347542160143184818391680, 1322291382391922104463259686181056293632
Offset: 0

Views

Author

Seiichi Manyama, Dec 02 2023

Keywords

Crossrefs

Cf. A052820, A367829.
Cf. A355086, A367830, A367845.

Programs

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

Formula

a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 2^(n-k) * (k-1)! * binomial(n,k) * a(n-k).
Showing 1-5 of 5 results.

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