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.

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A134175 a(n) = (32/2)*(n-1)*(n-2)*(n-3)*(n-4).

Original entry on oeis.org

0, 0, 0, 0, 384, 1920, 5760, 13440, 26880, 48384, 80640, 126720, 190080, 274560, 384384, 524160, 698880, 913920, 1175040, 1488384, 1860480, 2298240, 2808960, 3400320, 4080384, 4857600, 5740800, 6739200, 7862400, 9120384, 10523520, 12082560, 13808640, 15713280
Offset: 1

Views

Author

N. J. A. Sloane, Jan 30 2008

Keywords

Crossrefs

Cf. A052762.

Programs

  • Mathematica
    LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 0, 0, 384} , 50] (* or *) Table[(32/2)*(n-1)*(n-2)*(n-3)*(n-4), {n,1,50}] (* G. C. Greubel, May 30 2016 *)
  • PARI
    a(n) = 16*(n-1)*(n-2)*(n-3)*(n-4) \\ Michel Marcus, Jun 27 2013

Formula

G.f.: 384*x^5/(1-x)^5. - Colin Barker, Aug 28 2012

A154128 a(n) = 5^n*(n+4)!/n!.

Original entry on oeis.org

24, 600, 9000, 105000, 1050000, 9450000, 78750000, 618750000, 4640625000, 33515625000, 234609375000, 1599609375000, 10664062500000, 69726562500000, 448242187500000, 2838867187500000, 17742919921875000, 109588623046875000
Offset: 0

Views

Author

Omar E. Pol, Jan 05 2009

Keywords

Comments

Column 4 of square array A152818.

Crossrefs

Programs

  • Magma
    [5^n*(n+4)*(n+3)*(n+2)*(n+1): n in [0..20]]; // Vincenzo Librandi, Aug 15 2011
  • Mathematica
    LinearRecurrence[{25, -250, 1250, -3125, 3125}, {24, 600, 9000, 105000, 1050000}, 25] (* or *) Table[5^n*(n+4)*(n+3)*(n+2)*(n+1), {n,0,25}] (* G. C. Greubel, Sep 02 2016 *)

Formula

a(n) = 5^n*(n+4)*(n+3)*(n+2)*(n+1).
From R. J. Mathar, Feb 06 2009: (Start)
a(n) = A052762(n+4)*A000351(n).
a(n) = 24*A036071(n).
G.f: 24/(1-5*x)^5. (End)
From G. C. Greubel, Sep 02 2016: (Start)
a(n) = 25*a(n-1) - 250*a(n-2) + 1250*a(n-3) - 3125*a(n-4) + 3125*a(n-5).
E.g.f.: (24 + 480*x + 1800*x^2 + 2000*x^3 + 625*x^4)*exp(5*x). (End)

Extensions

More terms from R. J. Mathar, Feb 06 2009

A276161 Numbers that are the product of 4 consecutive positive numbers and the product of 2 nontrivial oblong numbers.

Original entry on oeis.org

840, 5040, 11880, 175560, 570024, 5997600, 34234200, 70073640, 569729160, 1262451960, 6643717080, 6927399360, 59312218680, 657557188200, 1288881113520, 7994422608480, 9803968814640, 73148660184600, 130903460103024, 250036769127600, 1081389616791120
Offset: 1

Views

Author

Gionata Neri and Cristina Gregorini, Aug 22 2016

Keywords

Examples

			175560 = 19*20*21*22 = 5*6*76*77 = 30*5852.
		

Crossrefs

Extensions

a(15)-a(21) from Jon E. Schoenfield, Nov 12 2016

A277444 Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the Möbius ladder M_k on 2k vertices.

Original entry on oeis.org

0, 0, 2, 0, 0, 6, 0, 2, 0, 12, 0, 0, 42, 24, 20, 0, 2, 48, 420, 120, 30, 0, 0, 306, 2160, 2420, 360, 42, 0, 2, 600, 17532, 27600, 9750, 840, 56, 0, 0, 2442, 115464, 375260, 191760, 30702, 1680, 72, 0, 2, 6048, 830100, 4810680, 4098510, 917280, 81032, 3024, 90, 0, 0, 20706, 5745120, 62813540, 85691640, 28669662, 3406368, 187560, 5040, 110
Offset: 1

Views

Author

Jeremy Tan, Oct 15 2016

Keywords

Comments

M_1 is two vertices connected by a triple edge and thus behaves like the path graph P_2 in terms of colorings. M_2 is isomorphic to K_4, the tetrahedral graph.

Examples

			Square array A(n,k) begins:
0,    0,    0,      0,       0,        0,          0, ...
2,    0,    2,      0,       2,        0,          2, ...
6,    0,   42,     48,     306,      600,       2442, ...
12,  24,  420,   2160,   17532,   115464,     830100, ...
20, 120, 2420,  27600,  375260,  4810680,   62813540, ...
30, 360, 9750, 191760, 4098510, 85691640, 1801468230, ...
		

Crossrefs

Cf. A277443 (colorings of prism graphs), A182406 (square grid graphs).
Columns k=1,2 are A002378 and A052762. Rows n=1,2 are A000004 and A010673.

Formula

A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k-(1-n)^k)-1.

A052768 a(n) = n*(n-1)*(n-2)*(n-3) for n>=5.

Original entry on oeis.org

0, 0, 0, 0, 0, 120, 360, 840, 1680, 3024, 5040, 7920, 11880, 17160, 24024, 32760, 43680, 57120, 73440, 93024, 116280, 143640, 175560, 212520, 255024, 303600, 358800, 421200, 491400, 570024, 657720, 755160, 863040, 982080, 1113024
Offset: 0

Views

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

Comments

Old name was: A simple grammar.

Crossrefs

Essentially the same as A052762.

Programs

  • Maple
    spec := [S,{B=Set(Z,1 <= card),S=Prod(Z,Z,Z,Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Formula

a(n)=0, n <= 4; a(n) = n*(n-1)*(n-2)*(n-3), n >= 5.
G.f.: 24*x^5*(5-10*x+10*x^2-5*x^3+x^4)/(1-x)^5. - Colin Barker, Jun 25 2012

Extensions

More terms and corrected formula from Larry Reeves (larryr(AT)acm.org), Jan 23 2001
Previous Showing 31-35 of 35 results.