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.

A379933 Expansion of e.g.f. 1/( exp(-x) - x )^2.

Original entry on oeis.org

1, 4, 22, 158, 1408, 15002, 186100, 2634998, 41937136, 741170834, 14402727484, 305225470046, 7005711916840, 173134991854970, 4583675648417044, 129424786945875398, 3882446011526729440, 123304773913531035170, 4133369745467043807340, 145840627118145774415214
Offset: 0

Views

Author

Seiichi Manyama, Jan 06 2025

Keywords

Links

Crossrefs

Cf. A072597, A379942, A379943.
Cf. A379934, A379936.
Cf. A358738, A377529.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x)-x)^2))
  • PARI
    a(n) = n!*sum(k=0, n, (k+1)*(k+2)^(n-k)/(n-k)!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A072597.
a(n) = n! * Sum_{k=0..n} (k+1) * (k+2)^(n-k)/(n-k)!.

A379934 E.g.f. A(x) satisfies A(x) = 1/( exp(-x*A(x)) - x )^2.

Original entry on oeis.org

1, 4, 38, 626, 15008, 476122, 18864124, 898099526, 49988162672, 3187006372466, 229091274174404, 18335328399262030, 1617287276785929928, 155893591123924724618, 16304903025947743812476, 1839154613521698544945238, 222562344165125395485931232, 28763041177430039602579211746
Offset: 0

Views

Author

Seiichi Manyama, Jan 06 2025

Keywords

Crossrefs

Cf. A379933, A379936.
Cf. A379864, A379884.

Programs

  • PARI
    a(n) = 2*n!*sum(k=0, n, (n+k+2)^(k-1)*binomial(n+k+2, n-k)/k!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A379884.
a(n) = 2 * n! * Sum_{k=0..n} (n+k+2)^(k-1) * binomial(n+k+2,n-k)/k!.

A379940 E.g.f. A(x) satisfies A(x) = 1/( exp(-x*A(x)^(2/3)) - x*A(x)^(1/3) )^3.

Original entry on oeis.org

1, 6, 81, 1788, 55785, 2267298, 114015825, 6848257272, 478929874257, 38253577287870, 3437561332041969, 343381977748134900, 37755068758105209849, 4531920849132497127258, 589779214651388664049905, 82722149483353129407482352, 12440903535778778244423710625, 1997259670949248788135594940278
Offset: 0

Views

Author

Seiichi Manyama, Jan 07 2025

Keywords

Crossrefs

Cf. A377892, A379936.

Programs

  • PARI
    a(n) = 3*n!*sum(k=0, n, (2*n+3)^(k-1)*binomial(2*n+3, n-k)/k!);

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377892.
a(n) = 3 * n! * Sum_{k=0..n} (2*n+3)^(k-1) * binomial(2*n+3,n-k)/k!.
a(n) == 0 (mod 3) for n>0.
Showing 1-3 of 3 results.

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

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