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.

A285270 a(n) = H_n(n), where H_n is the physicist's n-th Hermite polynomial.

Original entry on oeis.org

1, 2, 14, 180, 3340, 80600, 2389704, 83965616, 3409634960, 157077960480, 8093278209760, 461113571640128, 28784033772836544, 1953535902100115840, 143219579014652040320, 11279408109860685024000, 949705205977314865582336, 85131076752851318807814656, 8094279370190580822082014720
Offset: 0

Views

Author

Natan Arie Consigli, May 24 2017

Keywords

Examples

			Knowing that H_3(x) = 8x^3-12x, a(3) = H_3(3) = 8*3^3-12*3 = 180.

Links

Crossrefs

Cf. A089466 (probabilist's variant).
Cf. A349066, A349067, A349068, A349069.

Programs

  • Mathematica
    Table[HermiteH[n, n], {n, 0, 18}] (* Michael De Vlieger, May 25 2017 *)
  • PARI
    a(n) = polhermite(n, n); \\ Michel Marcus, May 25 2017
  • Python
    from sympy import hermite
def a(n): return hermite(n, n) # Indranil Ghosh, May 25 2017

Formula

a(n) ~ exp(-1/4) * 2^n * n^n. - Vaclav Kotesovec, Nov 07 2021

Extensions

More terms from Michel Marcus, May 25 2017

A349066 a(n) = H(2*n, n), where H(n,x) is n-th Hermite polynomial.

Original entry on oeis.org

1, 2, 76, 14136, 5324432, 3275529760, 2982971060928, 3773262142004096, 6332628384952750336, 13620318069121988018688, 36536710970888029776972800, 119598502032157660592768038912, 469232422933986002753883881312256, 2173747962477936168042899607178059776
Offset: 0

Views

Author

Vaclav Kotesovec, Nov 07 2021

Keywords

Links

Crossrefs

Cf. A285270, A349067, A349068.

Programs

  • Maple
    a:= n-> simplify(HermiteH(2*n, n)):
seq(a(n), n=0..20);  # Alois P. Heinz, Nov 07 2021
  • Mathematica
    Table[HermiteH[2*n, n], {n, 0, 15}]
  • PARI
    a(n) =  polhermite(2*n, n); \\ Michel Marcus, Nov 07 2021

Formula

a(n) ~ exp(-1) * 2^(2*n) * n^(2*n).

A349069 a(n) = H(n, 3*n), where H(n,x) is n-th Hermite polynomial.

Original entry on oeis.org

1, 6, 142, 5724, 324876, 23761800, 2126627016, 225081383184, 27498818692752, 3808595968290144, 589662462800129760, 100917872425324633536, 18918488805502510634688, 3855242696428245589623936, 848531650317994634533024896, 200604383862593153678170272000
Offset: 0

Views

Author

Vaclav Kotesovec, Nov 07 2021

Keywords

Comments

In general, for k>=1, H(n,k*n) ~ exp(-1/(4*k^2)) * (2*k)^n * n^n.

Links

Crossrefs

Cf. A285270, A349067, A349068.

Programs

  • Maple
    a:= n-> simplify(HermiteH(n, 3*n)):
seq(a(n), n=0..20);  # Alois P. Heinz, Nov 07 2021
  • Mathematica
    Table[HermiteH[n, 3*n], {n, 0, 20}]

Formula

a(n) ~ exp(-1/36) * 6^n * n^n.
Showing 1-3 of 3 results.

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

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