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 1-7 of 7 results.

A330150 Expansion of e.g.f. exp(-x) / (1 - log(1 + x)).

Original entry on oeis.org

1, 0, 0, 1, -1, 8, -16, 159, -659, 6824, -46680, 517581, -4941685, 61043344, -735256328, 10269016939, -147207286503, 2322683458544, -38298239486672, 677630804946393, -12581447014620585, 247342217288517496, -5096876494438056928, 110338442309322274295
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 03 2019

Keywords

Comments

Inverse binomial transform of A006252.

Crossrefs

Cf. A052841, A330149.
Cf. A006252, A291981.

Programs

  • Mathematica
    nmax = 23; CoefficientList[Series[Exp[-x]/(1 - Log[1 + x]), {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * A006252(k).
a(n) = (-1)^n + Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Dec 19 2023

A368283 Expansion of e.g.f. exp(2*x) / (1 + log(1 - x)).

Original entry on oeis.org

1, 3, 11, 52, 320, 2486, 23402, 258252, 3263528, 46433648, 734322672, 12776283136, 242519067056, 4987324250416, 110454579648688, 2621008072506592, 66341399843669760, 1784150447268259456, 50804574646886197888, 1527058892582680257024
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A007840, A291979, A330149, A368284.
Cf. A368285.

Programs

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

Formula

a(n) = 2^n + Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ n! * exp(n + 2 - 2*exp(-1)) / (exp(1) - 1)^(n+1). - Vaclav Kotesovec, Dec 29 2023

A368284 Expansion of e.g.f. exp(-2*x) / (1 + log(1 - x)).

Original entry on oeis.org

1, -1, 3, 0, 32, 182, 1882, 20500, 260136, 3701968, 58565360, 1019110848, 19346296752, 397867297136, 8811800026928, 209100451072672, 5292665533921024, 142338738348972672, 4053176346277660288, 121828547313861426176, 3854597854165079424768
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2023

Keywords

Crossrefs

Cf. A007840, A291979, A330149, A368283.

Programs

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

Formula

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

A368446 Expansion of e.g.f. exp(-x) / (1 + log(1 - 2*x)).

Original entry on oeis.org

1, 1, 9, 81, 1025, 16177, 306793, 6791201, 171849153, 4892782241, 154792866953, 5387090968113, 204528939571521, 8412441383512657, 372629008281155177, 17684630326318986881, 895251144144309285505, 48152984520621412552257
Offset: 0

Views

Author

Seiichi Manyama, Dec 24 2023

Keywords

Crossrefs

Cf. A330149, A368447.
Cf. A368286.

Programs

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

Formula

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

A368447 Expansion of e.g.f. exp(-x) / (1 + log(1 - 3*x)).

Original entry on oeis.org

1, 2, 22, 305, 5767, 136526, 3883258, 128933255, 4893787021, 208996349714, 9917947451590, 517743558041981, 29485295251306867, 1819129033610512958, 120867373194394631242, 8604378456170991789779, 653370570548903023444249, 52714379598185711313436226
Offset: 0

Views

Author

Seiichi Manyama, Dec 24 2023

Keywords

Crossrefs

Cf. A330149, A368446.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+sum(j=1, i, 3^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

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

A368451 Expansion of e.g.f. exp(-x) / (1 + log(1 - 2*x)/2).

Original entry on oeis.org

1, 0, 3, 16, 149, 1688, 23159, 371880, 6840553, 141780944, 3268764075, 82963535136, 2298431319293, 69012013452328, 2232249540339103, 77380297793229304, 2861727518793423057, 112465175425532789792, 4680372635423718547027, 205618540216497929458608
Offset: 0

Views

Author

Seiichi Manyama, Dec 24 2023

Keywords

Crossrefs

Cf. A330149, A368452.

Programs

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

Formula

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

A368452 Expansion of e.g.f. exp(-x) / (1 + log(1 - 3*x)/3).

Original entry on oeis.org

1, 0, 4, 29, 351, 5288, 96844, 2084787, 51569293, 1440778760, 44860522140, 1540040695961, 57780774428299, 2351977512750864, 103224895866407236, 4858737892917301679, 244142543354321358297, 13043294582176082455088, 738250195765281754969108
Offset: 0

Views

Author

Seiichi Manyama, Dec 24 2023

Keywords

Crossrefs

Cf. A330149, A368451.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+sum(j=1, i, 3^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

a(n) = (-1)^n + Sum_{k=1..n} 3^(k-1) * (k-1)! * binomial(n,k) * a(n-k).
Showing 1-7 of 7 results.

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

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