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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, 5654880, 6538455, 7529130 (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 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 *) 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

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)