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 1-5 of 5 results.

A247851 The 6th Hermite Polynomial evaluated at n: H_6(n) = 64*n^6-480*n^4+720*n^2-120.

Original entry on oeis.org

-120, 184, -824, 14136, 150664, 717880, 2389704, 6412216, 14857096, 30921144, 59271880, 106439224, 181253256, 295328056, 463591624, 704861880, 1042468744, 1504922296, 2126627016, 2948642104, 4019487880, 5395998264, 7144219336, 9340353976, 12071752584
Offset: 0

Views

Author

Vincenzo Librandi, Sep 25 2014

Keywords

Links

Crossrefs

Cf. similar sequences listed in A247850.

Programs

  • Magma
    [64*n^6-480*n^4+720*n^2-120: n in [0..30]];
  • Magma
    I:=[-120,184,-824,14136,150664,717880,2389704]; [n le 7 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..30]];
  • Mathematica
    Table[64 n^6 - 480 n^4 + 720 n^2 - 120, {n, 0, 30}] (* or *) CoefficientList[Series[(-120 + 1024 x -4632 x^2 + 27968 x^3 + 23768 x^4 - 2112 x^5 + 184 x^6)/(1-x)^7, {x, 0, 30}], x]
LinearRecurrence[{7,-21,35,-35,21,-7,1},{-120,184,-824,14136,150664,717880,2389704},30] (* Harvey P. Dale, Apr 08 2019 *)
  • PARI
    a(n)=polhermite(6,n) \\ Charles R Greathouse IV, Jan 29 2016
  • Python
    from sympy import hermite
def A247851(n): return hermite(6,n) # Chai Wah Wu, Jan 06 2022

Formula

G.f.: (-120 + 1024*x - 4632*x^2 + 27968*x^3 + 23768*x^4 -2112* x^5 + 184*x^6)/(1-x)^7.
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).

A247852 The 7th Hermite Polynomial evaluated at n: H_7(n) = 128*n^7 -1344*n^5 + 3360*n^3 - 1680*n.

Original entry on oeis.org

0, 464, -3104, 39024, 929216, 6211600, 26096544, 83965616, 226102144, 535292496, 1148943200, 2282359024, 4257827136, 7540152464, 12779289376, 20860714800, 32964187904, 50631541456, 75844149984, 111110719856, 159566046400, 225081383184, 312387068576
Offset: 0

Views

Author

Vincenzo Librandi, Sep 25 2014

Keywords

Links

Crossrefs

Cf. similar sequences listed in A247850.

Programs

  • Magma
    [128*n^7-1344*n^5+3360*n^3-1680*n: n in [0..30]];
  • Magma
    I:=[0,464,-3104,39024,929216,6211600,26096544,83965616]; [n le 8 select I[n] else 8*Self(n-1)-28*Self(n-2)+56*Self(n-3)-70*Self(n-4)+56*Self(n-5)-28*Self(n-6)+8*Self(n-7)-Self(n-8): n in [1..30]];
  • Mathematica
    Table[128 n^7 - 1344 n^5 + 3360 n^3 - 1680 n, {n, 0, 30}] (* or *) CoefficientList[Series[x (464 - 6816 x + 76848 x^2 + 504128 x^3 + 76848 x^4 - 6816 x^5 + 464 x^6)/(1-x)^8, {x, 0, 30}], x]
  • PARI
    a(n)=polhermite(7,n) \\ Charles R Greathouse IV, Jan 29 2016
  • Python
    from sympy import hermite
def A247852(n): return hermite(7, n) # Chai Wah Wu, Jan 06 2022

Formula

G.f.: x*(464-6816*x+76848*x^2+504128*x^3+76848*x^4-6816*x^5 +464*x^6)/(1-x)^8.
a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8).

A247853 The 8th Hermite Polynomial evaluated at n: H_8(n) = 256*n^8-3584*n^6+13440*n^4-13440*n^2+1680.

Original entry on oeis.org

1680, -1648, -880, 36240, 5324432, 52065680, 279702672, 1085747600, 3409634960, 9202368912, 22149057680, 48721749392, 99650305680, 191909371280, 351329819792, 615953377680, 1040259450512, 1700403497360, 2700616621200, 4180926365072, 6326369025680
Offset: 0

Views

Author

Vincenzo Librandi, Sep 25 2014

Keywords

Links

Crossrefs

Cf. similar sequences listed in A247850.

Programs

  • Magma
    [256*n^8-3584*n^6+13440*n^4-13440*n^2+1680: n in [0..30]];
  • Magma
    I:=[1680,-1648,-880,36240,5324432, 52065680,279702672,1085747600,3409634960]; [n le 9 select I[n] else 9*Self(n-1)-36*Self(n-2)+84*Self(n-3)-126*Self(n-4)+126*Self(n-5)-84*Self(n-6)+36*Self(n-7)-9*Self(n-8)+Self(n-9): n in [1..30]];
  • Mathematica
    Table[256 n^8 - 3584 n^6 + 13440 n^4 - 13440 n^2 + 1680, {n, 0, 30}] (* or *) CoefficientList[Series[(1680 - 16768 x + 74432 x^2 - 156288 x^3 + 5316704 x^4 + 5105024 x^5 - 15168 x^6 + 13952 x^7 - 1648 x^8)/(1 - x)^9, {x, 0, 30}],x]
  • PARI
    a(n)=polhermite(8,n) \\ Charles R Greathouse IV, Jan 29 2016
  • Python
    from sympy import hermite
def A247853(n): return hermite(8,n) # Chai Wah Wu, Jan 06 2022

Formula

G.f.: (1680-16768*x+74432*x^2-156288*x^3+5316704*x^4 +5105024*x^5-15168*x^6+13952*x^7-1648*x^8)/(1-x)^9.
a(n) = 9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9).

A247854 The 9th Hermite Polynomial evaluated at n: H_9(n) = 512*n^9 - 9216*n^7 + 48384*n^5 - 80640*n^3 + 30240*n.

Original entry on oeis.org

0, -10720, 46144, -406944, 27728000, 421271200, 2938887360, 13857016544, 50936525056, 157077960480, 424598062400, 1035360742240, 2323482102144, 4869001213856, 9632766324160, 18144829893600, 32760875409920, 57003614246944, 96008691963456, 157097430355040
Offset: 0

Views

Author

Vincenzo Librandi, Sep 26 2014

Keywords

Links

Crossrefs

Cf. similar sequences listed in A247850.

Programs

  • Mathematica
    Table[512 n^9 - 9216 n^7 + 48384 n^5 - 80640 n^3 + 30240 n, {n, 0, 30}]
  • PARI
    a(n)=polhermite(9,n) \\ Charles R Greathouse IV, Jan 29 2016
  • Python
    from sympy import hermite
def A247854(n): return hermite(9,n) # Chai Wah Wu, Jan 06 2022

Formula

G.f.: -x*(10720-153344*x+1350784*x^2-35160320*x^3-117890240* x^4-35160320*x^5+1350784*x^6-153344*x^7+10720*x^8)/(x-1)^10.
a(n) = 10*a(n-1)-45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10).

A247855 The 10th Hermite Polynomial evaluated at n: H_10(n) = 1024*n^10 - 23040*n^8 + 161280*n^6 - 403200*n^4 + 302400*n^2 - 30240.

Original entry on oeis.org

-30240, 8224, 200416, -3093984, 125984224, 3275529760, 30232000224, 174454774816, 753610971616, 2661760648224, 8093278209760, 21900944840224, 53969864949216, 123139662877216, 263393520320224, 533257736009760, 1029623343008224, 1907515621443616
Offset: 0

Views

Author

Vincenzo Librandi, Sep 26 2014

Keywords

Links

Crossrefs

Cf. similar sequences listed in A247850.

Programs

  • Magma
    [1024*n^10-23040*n^8+161280*n^6-403200*n^4 +302400*n^2-30240: n in [0..30]];
  • Magma
    I:=[-30240, 8224,200416,-3093984,125984224,3275529760,30232000224, 174454774816,753610971616,2661760648224,8093278209760]; [n le 11 select I[n] else 11*Self(n-1)-55*Self(n-2)+165*Self(n-3)-330*Self(n-4)+462*Self(n-5)-462*Self(n-6)+330*Self(n-7)-165*Self(n-8)+55*Self(n-9)-11*Self(n-10)+Self(n-11): n in [1..30]];
  • Mathematica
    Table[1024 n^10 - 23040 n^8 + 161280 n^6 - 403200 n^4 + 302400 n^2 - 30240, {n, 0, 30}] (* or *) CoefficientList[Series[(-30240 + 340864 x - 1553248 x^2 + 143360 x^3 + 159704768 x^4 + 1703150336 x^5 + 1689179456 x^6 + 169683968 x^7 - 4846240 x^8 + 109952 x^9 + 8224 x^10)/(1-x)^11, {x, 0, 30}], x]
  • PARI
    a(n)=polhermite(10,n) \\ Charles R Greathouse IV, Jan 29 2016
  • Python
    m = [3715891200, -16721510400, 30036787200, -27095040000, 12533391360, -2612736000, 139499520, 3640320, 153728, -38464, -30240]
A247855_list = [m[-1]]
for _ in range(10**1):
    for i in range(10):
        m[i+1]+= m[i]
    A247855_list.append(m[-1]) # Chai Wah Wu, Nov 09 2014

Formula

G.f.: (-30240+340864*x-1553248*x^2+143360*x^3+159704768*x^4 +1703150336*x^5+1689179456*x^6+169683968*x^7-4846240*x^8 +109952*x^9+8224*x^10)/(1-x)^11.
a(n) = 11*a(n-1)-55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)-165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11).
Showing 1-5 of 5 results.

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

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