A082037 -id:A082037 - cp's OEIS frontend

A082033 a(n) = (3n+1)*n!.

1, 4, 14, 60, 312, 1920, 13680, 110880, 1008000, 10160640, 112492800, 1357171200, 17723059200, 249080832000, 3748666521600, 60153020928000, 1025216704512000, 18495746260992000, 352130553815040000, 7055415823712256000

Offset: 0

Paul Barry, Apr 02 2003

A row of the number array A082037.

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014

Cf. A007680, A082034.

[(3*n+1)*Factorial(n): n in [0..20]]; // Vincenzo Librandi, May 09 2011

a(n) = A016777(n)*n!.

3*a(n) +(-3*n-5)*a(n-1) +2*(n-1)*a(n-2)=0. - R. J. Mathar, Oct 29 2014

A082034 a(n) = (4n + 1)n!.

Original entry on oeis.org

1, 5, 18, 78, 408, 2520, 18000, 146160, 1330560, 13426560, 148780800, 1796256000, 23471078400, 330032102400, 4969162598400, 79768136448000, 1359981342720000, 24542432538624000, 467373280518144000, 9366672731480064000

Offset: 0

Paul Barry, Apr 02 2003

A row of the array A082037.

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Cf. A082033, A007680.

[(4*n+1)*Factorial(n) : n in [0..20]]; // Vincenzo Librandi, Sep 22 2011

Table[(4n+1)n!,{n,0,20}] (* Harvey P. Dale, Mar 02 2022 *)

a(n) = A016813(n)*n!.
(-4*n+3)*a(n) + n*(4*n+1)*a(n-1) = 0. - R. J. Mathar, Nov 07 2014
4*a(n) + (-4*n-7)*a(n-1) + 3*(n-1)*a(n-2) = 0. - R. J. Mathar, Nov 07 2014

A082038 A square array of quadratic-factorial numbers, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 3, 2, 1, 7, 14, 6, 1, 13, 42, 78, 24, 1, 21, 86, 258, 504, 120, 1, 31, 146, 546, 1752, 3720, 720, 1, 43, 222, 942, 3768, 13320, 30960, 5040, 1, 57, 314, 1446, 6552, 28920, 113040, 287280, 40320, 1, 73, 422, 2058, 10104, 50520, 246960, 1063440

Offset: 0

Paul Barry, Apr 02 2003

Rows include A000142, A001564, A082035, A082036.

			Rows begin
1 1 2 6 24 ...
1 3 14 78 504 ...
1 7 42 258 1752 ...
1 13 86 546 3768 ...
1 21 146 942 6552 ...

Cf. A082037, A082039.

Square array defined by T(n, k)=((kn)^2+kn+1)n!

A082042 a(n) = (n^2+1)*n!.

Original entry on oeis.org

1, 2, 10, 60, 408, 3120, 26640, 252000, 2620800, 29756160, 366508800, 4869849600, 69455232000, 1058593536000, 17174123366400, 295534407168000, 5377157001216000, 103149354147840000, 2080771454361600000

Offset: 0

Paul Barry, Apr 02 2003

Main diagonal of A082037
a(n) = total number of runs when each permutation on [n+1] is split into maximal monotone runs. (A monotone run is a sequence of consecutive entries whose differences are all 1 or all -1. Example: 34-1-765-2 contributes 4 runs to a(6) as indicated.) - David Callan, Nov 16 2003
a(n) is also the number of distinct planar embeddings of the (n+1)-Sierpinski gasket graph. - Eric W. Weisstein, May 21 2024

Eric Weisstein's World of Mathematics, Planar Embedding.
Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.

Cf. A018932. [From R. J. Mathar, Dec 15 2008]

Cf. A000142, A002522, A082037.

a(n) = A002522(n)*A000142(n).

D-finite with recurrence (n^2-2*n+2)*a(n) -n*(n^2+1)*a(n-1)=0. - R. J. Mathar, Dec 03 2014

cp's OEIS Frontend

A082033 a(n) = (3n+1)*n!.

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A082034 a(n) = (4n + 1)n!.

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A082038 A square array of quadratic-factorial numbers, read by antidiagonals.

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A082042 a(n) = (n^2+1)*n!.

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cp's OEIS Frontend

A082033 a(n) = (3n+1)*n!.

Views

Author

Keywords

Comments

Links

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Programs

Magma

Formula

A082034 a(n) = (4*n + 1)*n!.

Views

Author

Keywords

Comments

Links

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Programs

Magma

Mathematica

Formula

A082038 A square array of quadratic-factorial numbers, read by antidiagonals.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A082042 a(n) = (n^2+1)*n!.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A082034 a(n) = (4n + 1)n!.