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.

A362654 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x) ).

Original entry on oeis.org

1, 1, 3, 22, 197, 2316, 33967, 595624, 12190761, 285479056, 7531645211, 221124649824, 7152276636397, 252742471065280, 9688895208298503, 400510408002257536, 17759663471017945553, 840937887639033467136, 42351198256293556043827
Offset: 0

Views

Author

Seiichi Manyama, Apr 28 2023

Keywords

Links

Crossrefs

Cf. A273954, A362655.
Cf. A362653, A362673.

Programs

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

Formula

E.g.f.: exp( -LambertW(-x * exp(x^2)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (n-2*k+1)^(n-2*k-1) / (k! * (n-2*k)!).
a(n) ~ sqrt(1 + LambertW(2*exp(-2))) * 2^(n/2) * n^(n-1) / (exp(n-1) * LambertW(2*exp(-2))^(n/2)). - Vaclav Kotesovec, Aug 05 2025

A362674 E.g.f. satisfies A(x) = exp( x * exp(x^3) / A(x) ).

Original entry on oeis.org

1, 1, -1, 4, -3, 136, -1685, 26496, -433783, 8415856, -184328649, 4515376240, -121983339731, 3605788384056, -115769790754813, 4012378854562456, -149305859447213295, 5937271828722146656, -251273782851599681297, 11276632158754470014304
Offset: 0

Views

Author

Seiichi Manyama, Apr 29 2023

Keywords

Links

Crossrefs

Cf. A362673.

Programs

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

Formula

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

A362653 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x)^2 ).

Original entry on oeis.org

1, 1, 5, 55, 849, 17641, 462373, 14651295, 545025281, 23291218801, 1124589371301, 60553038168679, 3597677815336465, 233810179507710105, 16499939198003013509, 1256544674435523638671, 102713141497515307408257, 8970278754666722087785825
Offset: 0

Views

Author

Seiichi Manyama, Apr 28 2023

Keywords

Links

Crossrefs

Cf. A360547, A362654, A362673.

Programs

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

Formula

E.g.f.: exp( -LambertW(-2*x * exp(x^2))/2 ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (2*n-4*k+1)^(n-2*k-1) / (k! * (n-2*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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