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.

A365056 E.g.f. satisfies A(x) = exp( x * (1+x/2)/A(x) ).

Original entry on oeis.org

1, 1, 0, 1, -6, 46, -440, 5076, -68740, 1070056, -18835164, 369994780, -8025080096, 190501729848, -4912802070280, 136775150153656, -4088669684755440, 130620500241909376, -4441243727496127184, 160132524268963159440, -6102784264210449418144
Offset: 0

Views

Author

Seiichi Manyama, Aug 19 2023

Keywords

Links

Crossrefs

Cf. A365053, A365054, A365055.
Cf. A365038.

Programs

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

Formula

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

A365039 E.g.f. satisfies A(x) = exp(x * (1 + x)/A(x)^2).

Original entry on oeis.org

1, 1, -1, 7, -79, 1201, -22961, 530167, -14372191, 447825889, -15776617249, 620209389031, -26918670325295, 1278598424153233, -65973615445792081, 3674793950748867031, -219773335672937703871, 14046128883828030510529, -955409650156763223984449
Offset: 0

Views

Author

Seiichi Manyama, Aug 18 2023

Keywords

Links

Crossrefs

Cf. A362771, A362773, A363478, A365038, A365040.
Cf. A361068.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(2*x*(1+x))/2)))

Formula

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

A365040 E.g.f. satisfies A(x) = exp(x * (1 + x)/A(x)^3).

Original entry on oeis.org

1, 1, -3, 34, -623, 15636, -499277, 19382686, -886663647, 46716323752, -2786249779829, 185574001203834, -13652735530485647, 1099602989008154476, -96230900016000250269, 9092834662610587023286, -922622745817066477888703, 100054409045940667152740304
Offset: 0

Views

Author

Seiichi Manyama, Aug 18 2023

Keywords

Links

Crossrefs

Cf. A362771, A362773, A363478, A365038, A365039.
Cf. A361069.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(3*x*(1+x))/3)))

Formula

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