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.

A362480 E.g.f. satisfies A(x) = exp(x - x^2 * A(x)^2).

Original entry on oeis.org

1, 1, -1, -17, -47, 961, 14191, -35825, -4258463, -46744703, 1252890271, 49630926511, 61171154353, -41944148256191, -1033550755723121, 24977027757497551, 2117415434541888961, 20487158235798909697, -3240242006475108681665, -146763820123398901335185
Offset: 0

Views

Author

Seiichi Manyama, Apr 21 2023

Keywords

Links

Crossrefs

Cf. A362481, A362482.
Cf. A143768, A362492.

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) = sqrt( LambertW(2*x^2 * exp(2*x))/(2*x^2) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * (2*k+1)^(n-k-1) / (k! * (n-2*k)!).

A362494 E.g.f. satisfies A(x) = exp(x - x^4/4 * A(x)^4).

Original entry on oeis.org

1, 1, 1, 1, -5, -149, -2249, -26249, -251159, -1443959, 21646801, 1209344401, 35457894451, 817789456771, 14796993881671, 137893562065351, -4661597156689199, -372730180154530799, -16419790692323174879, -559989133713039523679, -14492546886670841884949
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2023

Keywords

Links

Crossrefs

Cf. A362492, A362493.
Cf. A362491.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^4*exp(4*x))/4)))

Formula

E.g.f.: exp(x - LambertW(x^4 * exp(4*x))/4) = ( LambertW(x^4 * exp(4*x))/x^4 )^(1/4).
a(n) = n! * Sum_{k=0..floor(n/4)} (-1/4)^k * (4*k+1)^(n-3*k-1) / (k! * (n-4*k)!).

A362493 E.g.f. satisfies A(x) = exp(x - x^3/3 * A(x)^3).

Original entry on oeis.org

1, 1, 1, -1, -31, -319, -2279, -4199, 269473, 7155233, 114846641, 920526641, -18415853279, -1115017249631, -31675298017271, -526379460621559, 2394778195929281, 603748739138745281, 27895091311964499553, 769764386129113157473, 6164705700089328588481
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2023

Keywords

Links

Crossrefs

Cf. A362492, A362494.
Cf. A362478.

Programs

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

Formula

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

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

Content is available under The OEIS End-User License Agreement.