A151974 a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)/8.

0, 15, 90, 315, 840, 1890, 3780, 6930, 11880, 19305, 30030, 45045, 65520, 92820, 128520, 174420, 232560, 305235, 395010, 504735, 637560, 796950, 986700, 1210950, 1474200, 1781325, 2137590, 2548665, 3020640, 3560040, 4173840, 4869480, 5654880, 6538455, 7529130

Offset

0,2

Comments

Also the number of 4-cycles in the (n+3)-triangular graph. - Eric W. Weisstein, Aug 14 2017

Links

Table of n, a(n) for n=0..34.

Eric Weisstein's World of Mathematics, Graph Cycle.

Eric Weisstein's World of Mathematics, Johnson Graph.

Eric Weisstein's World of Mathematics, Triangular Graph.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)/8.

G.f.: 15*x/(1-x)^6. - Colin Barker, Jun 25 2012

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Eric W. Weisstein, Aug 14 2017

From Amiram Eldar, Jan 09 2022: (Start)

Sum_{n>=1} 1/a(n) = 1/12.

Sum_{n>=1} (-1)^(n+1)/a(n) = 16*log(2)/3 - 131/36. (End)

Maple

A151974:=n->n*(n+1)*(n+2)*(n+3)*(n+4)/8: seq(A151974(n), n=0..60); # Wesley Ivan Hurt, Feb 11 2017

Mathematica

Table[Pochhammer[n, 5]/8, {n, 0, 31}] (* or *)
Rest @ CoefficientList[Series[15 x^2/(1 - x)^6, {x, 0, 32}], x] (* Michael De Vlieger, Feb 12 2017 *)
Pochhammer[Range[0, 20], 5]/8 (* Eric W. Weisstein, Aug 14 2017 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 15, 90, 315, 840, 1890}, 20] (* Eric W. Weisstein, Aug 14 2017 *)
Table[15 Binomial[n + 4, 5], {n, 0, 20}] (* Eric W. Weisstein, Aug 14 2017 *)
15 Binomial[Range[4, 24], 5] (* Eric W. Weisstein, Aug 14 2017 *)
Table[(24 n+50 n^2+35 n^3+10 n^4+n^5)/8, {n, 0, 40}] (* or *) Table[Times@@Range[n, n+4]/8, {n, 0, 40}] (* Harvey P. Dale, Mar 06 2024 *)

Prog

(PARI) a(n)=n*(n+1)*(n+2)*(n+3)*(n+4)/8 \\ Charles R Greathouse IV, Aug 14 2017

Crossrefs

Cf. A054559.

Cf. A002417 (number of 3-cycles in the triangular graph), A290939 (5-cycles), A290940 (6-cycles).

Sequence in context: A316224 A022707 A323334 * A179096 A328994 A001297

Adjacent sequences: A151971 A151972 A151973 * A151975 A151976 A151977

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Extensions

Offset corrected by Eric W. Weisstein, Aug 14 2017

Status

approved