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A151974 a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)/8. 4
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 (list; graph; refs; listen; history; text; internal format)
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..31.

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

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 *)

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 A001297 A005716

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

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)