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.

A081131 a(n) = n^(n-2) * binomial(n,2).

Original entry on oeis.org

0, 0, 1, 9, 96, 1250, 19440, 352947, 7340032, 172186884, 4500000000, 129687123005, 4086546038784, 139788510734886, 5159146026151936, 204350482177734375, 8646911284551352320, 389289535005334947848, 18580248257778920521728, 937146152681201173795569
Offset: 0

Views

Author

Paul Barry, Mar 08 2003

Keywords

Comments

Main diagonal of A081130.
a(n) is the number of partial functions f: {1,2,...,n} -> {1,2,...,n} that have exactly 2 undefined elements. - Geoffrey Critzer, Feb 08 2012
a(n+1) is the determinant of the circulant matrix having (n-1, n-2, ..., 0) as first row, for n >= 1. See A070896 for a variant, and A303260 for a related sequence. - M. F. Hasler, Apr 23 2018
a(n) is the number of birooted labeled trees on n nodes. - Brendan McKay, May 01 2018

Links

Crossrefs

Cf. A070896, A081129, A081130, A303260.
Sequences of the form (n+m)^n*binomial(n+2,2): A081133 (m=0), A081132 (m=1), this sequence (m=2), A053507 (m=3), A081196 (m=4).

Programs

  • Magma
    [n lt 2 select 0 else n^(n-2)*Binomial(n,2): n in [0..20]]; // G. C. Greubel, May 18 2021
  • Mathematica
    Join[{0},Table[n^(n-2) Binomial[n, 2], {n, 1, 20}]] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)
  • Sage
    [0 if (n<2) else n^(n-2)*binomial(n,2) for n in (0..20)] # G. C. Greubel, May 18 2021

Formula

a(0) = a(1) = 0, a(n) = n^(n-2)*binomial(n,2).
E.g.f.: T(x)^2/(2*(1-T(x))) where T(x) is the e.g.f. for A000169. - Geoffrey Critzer, Feb 08 2012

A081132 a(n) = (n+1)^n*binomial(n+2,2).

Original entry on oeis.org

1, 6, 54, 640, 9375, 163296, 3294172, 75497472, 1937102445, 55000000000, 1711870023666, 57954652913664, 2120125746145771, 83340051191685120, 3503151123046875000, 156797324626531188736, 7445162356977030877593
Offset: 0

Views

Author

Paul Barry, Mar 08 2003

Keywords

Comments

A diagonal of A081130.
a(n) is the sum of all the fixed points in the set of endofunctions on {1,2,...,n+1}, i.e., the functions f:{1,2,...,n+1} -> {1,2,...,n+1}. - Geoffrey Critzer, Sep 17 2011

Examples

			a(1) = 6 because there are four functions from {1,2} into {1,2}: (1*,1) (1*,2*) (2,1) (2,2*) and the fixed points (marked *) sum to 6.

Links

Crossrefs

Sequences of the form (n+m)^n*binomial(n+2,2): A081133 (m=0), this sequence (m=1), A081131 (m=2), A053507 (m=3), A081196 (m=4).

Programs

  • Magma
    [((n+1)^n*Binomial(n+2,2)): n in [0..20]]; // Vincenzo Librandi, Sep 21 2011
  • Maple
    seq((n+1)^n*binomial(n+2,2), n=0..20); # G. C. Greubel, May 18 2021
  • Mathematica
    Table[n^n*(n+1)/2,{n,20}]
  • Sage
    [(n+1)^n*binomial(n+2,2) for n in (0..20)] # G. C. Greubel, May 18 2021

Formula

a(n) = (n+1)^n*binomial(n+2,2).

A081133 a(n) = n^n*binomial(n+2, 2).

Original entry on oeis.org

1, 3, 24, 270, 3840, 65625, 1306368, 29647548, 754974720, 21308126895, 660000000000, 22254310307658, 811365140791296, 31801886192186565, 1333440819066961920, 59553569091796875000, 2822351843277561397248
Offset: 0

Views

Author

Paul Barry, Mar 08 2003

Keywords

Comments

A diagonal of A081130.

Links

Crossrefs

Sequences of the form (n+m)^n*binomial(n+2,2): this sequence (m=0), A081132 (m=1), A081131 (m=2), A053507 (m=3), A081196 (m=4).

Programs

  • Magma
    [(n^n*Binomial(n+2,2)): n in [0..20]]; // Vincenzo Librandi, Sep 22 2011
  • Maple
    seq(n^n*binomial(n+2,2), n=0..20); # G. C. Greubel, May 18 2021
  • Mathematica
    Join[{1},Table[n^n Binomial[n+2,2],{n,20}]] (* Harvey P. Dale, Dec 27 2011 *)
  • Sage
    [n^n*binomial(n+2,2) for n in (0..20)] # G. C. Greubel, May 18 2021

Formula

a(n) = n^n*(n+1)*(n+2)/2.
Showing 1-3 of 3 results.

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