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 1-3 of 3 results.

A360991 Expansion of e.g.f. exp(exp(x) - 1 + x^2/2).

Original entry on oeis.org

1, 1, 3, 8, 30, 117, 533, 2599, 13919, 79620, 487810, 3167265, 21744187, 157020697, 1189321019, 9417789650, 77774264012, 668233623419, 5961395449795, 55117233908411, 527263186773227, 5210880621612366, 53130216638022540, 558176360466846439
Offset: 0

Views

Author

Seiichi Manyama, Mar 14 2023

Keywords

Crossrefs

Cf. A097514, A355337, A361489.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp(x)-1+x^2/2)))

Formula

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

A361493 Expansion of e.g.f. exp(exp(x) - 1 + x^3).

Original entry on oeis.org

1, 1, 2, 11, 39, 172, 1163, 6547, 41772, 335139, 2486215, 20078610, 186139957, 1676540257, 16077206122, 168739976555, 1763716943267, 19358116589964, 226362412711759, 2669223655597955, 32748447519013132, 421204995451111971, 5496921281576148363
Offset: 0

Views

Author

Seiichi Manyama, Mar 14 2023

Keywords

Crossrefs

Cf. A355337, A361489.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp(x)-1+x^3)))

Formula

a(0) = a(1) = 1, a(2) = 2; a(n) = 6 * binomial(n-1,2) * a(n-3) + Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).

A361531 Expansion of e.g.f. exp(1 - exp(x) + x^3/6).

Original entry on oeis.org

1, -1, 0, 2, -3, -2, 21, -44, -62, 631, -1367, -3170, 34849, -86855, -302964, 3058342, -8509971, -36488802, 430842051, -1111575888, -6244999438, 78663444549, -250850311489, -1724880111306, 18475299723737, -65061274823853, -444914618968648, 6831921081061986
Offset: 0

Views

Author

Seiichi Manyama, Mar 14 2023

Keywords

Crossrefs

Cf. A293037, A337062.
Cf. A124504, A361489.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-exp(x)+x^3/6)))

Formula

a(0) = 1, a(1) = -1, a(2) = 0; a(n) = binomial(n-1,2) * a(n-3) - Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).
Showing 1-3 of 3 results.

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

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