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 1-4 of 4 results.

A363354 E.g.f. satisfies A(x) = exp(x * (1 + x * A(x)^3)).

Original entry on oeis.org

1, 1, 3, 25, 277, 4221, 81421, 1891429, 51638217, 1618907257, 57332786041, 2264047223241, 98641443498973, 4700569138096885, 243213757144477029, 13579261873673960941, 813757288951509415441, 52098716516012891238129, 3548972379593741013388657
Offset: 0

Views

Author

Seiichi Manyama, Aug 17 2023

Keywords

Links

Crossrefs

Cf. A125500, A143768, A363529.
Cf. A212917.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^2*exp(3*x))/3)))

Formula

E.g.f.: exp( x - LambertW(-3*x^2*exp(3*x))/3 ).
a(n) = n! * Sum_{k=0..n} (3*n-3*k+1)^(k-1) * binomial(k,n-k)/k!.

A365035 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).

Original entry on oeis.org

1, 1, 3, 1, -11, 61, 301, -6299, 7561, 903673, -9019079, -145636919, 4305630781, 7516191541, -2037845181371, 22442805921901, 944219385367441, -29922880660473359, -288352494154313999, 32071808922904896913, -273044292430852251899
Offset: 0

Views

Author

Seiichi Manyama, Aug 17 2023

Keywords

Links

Crossrefs

Cf. A125500, A143768, A363354, A363529, A365036, A365037.
Cf. A361090.

Programs

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

Formula

E.g.f.: exp( x + LambertW(x^2*exp(-x)) ).
a(n) = n! * Sum_{k=1..n} (-n+k+1)^(k-1) * binomial(k,n-k)/k! for n>0.

A365036 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^2)).

Original entry on oeis.org

1, 1, 3, -5, -23, 521, -1829, -71021, 1319697, 5905297, -683965709, 8664974891, 311864420473, -13981842414695, 6694007756619, 16448800124183491, -448649039951220959, -13236887251789967071, 1210629233913421852387, -12065049302884271631269
Offset: 0

Views

Author

Seiichi Manyama, Aug 17 2023

Keywords

Links

Crossrefs

Cf. A125500, A143768, A363354, A363529, A365035, A365037.
Cf. A361091.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(2*x^2*exp(-2*x))/2)))

Formula

E.g.f.: exp( x + LambertW(2*x^2*exp(-2*x))/2 ).
a(n) = n! * Sum_{k=0..n} (-2*n+2*k+1)^(k-1) * binomial(k,n-k)/k!.

A365037 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^3)).

Original entry on oeis.org

1, 1, 3, -11, -11, 1341, -14339, -168923, 8905065, -85313735, -4604578919, 197455645641, -273728455571, -267002430142187, 9427821270512373, 178475402982086701, -28273343910563670959, 713736314833387866225, 51907546734507018043057
Offset: 0

Views

Author

Seiichi Manyama, Aug 17 2023

Keywords

Links

Crossrefs

Cf. A125500, A143768, A363354, A363529, A365035, A365036.
Cf. A361092.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(3*x^2*exp(-3*x))/3)))

Formula

E.g.f.: exp( x + LambertW(3*x^2*exp(-3*x))/3 ).
a(n) = n! * Sum_{k=0..n} (-3*n+3*k+1)^(k-1) * binomial(k,n-k)/k!.
Showing 1-4 of 4 results.

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

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