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 A051836 a(n) = n*(n+1)*(n+2)*(n+3)*(3*n+2)/120. 14
 0, 1, 8, 33, 98, 238, 504, 966, 1716, 2871, 4576, 7007, 10374, 14924, 20944, 28764, 38760, 51357, 67032, 86317, 109802, 138138, 172040, 212290, 259740, 315315, 380016, 454923, 541198, 640088, 752928, 881144, 1026256, 1189881, 1373736 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 5-dimensional version of pentagonal-based pyramidal numbers. - Ben Creech (mathroxmysox(AT)yahoo.com) If Y is a 3-subset of an n-set X then, for n>=7, a(n-6) is the number of 7-subsets of X having at least two elements in common with Y. - Milan Janjic, Nov 23 2007 Antidiagonal sums of the convolution array A213548. - Clark Kimberling, Jun 17 2012 After 0, convolution of nonzero triangular numbers (A000217) and nonzero pentagonal numbers (A000326). - Bruno Berselli, Jun 27 2013 a(n) is also the number of odd chordless cycles in the graph complement of the (n+1)-Andrasfai graph. - Eric W. Weisstein, Apr 14 2017 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-8. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Andrasfai Graph Eric Weisstein's World of Mathematics, Chordless Cycle Eric Weisstein's World of Mathematics, Graph Complement Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = C(n+4, n)*(3n+5)/5. G.f.: x*(1+2*x)/(1-x)^6. (adapted by Vincenzo Librandi, Jul 04 2017) EXAMPLE By the fourth comment: A000217(1..6) and A000326(1..6) give the term a(6) = 1*21+5*15+12*10+22*6+35*3+51*1 = 504. - Bruno Berselli, Jun 27 2013 MAPLE with (combinat):a[0]:=0:for n from 1 to 50 do a[n]:=stirling2(n+2, n)+a[n-1] od: seq(a[n], n=0..34); # Zerinvary Lajos, Mar 17 2008 MATHEMATICA Table[n(n + 1)(n + 2)(n + 3)(3n + 2)/120, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *) CoefficientList[Series[x (1 + 2 x) / (1 - x)^6, {x, 0, 33}], x] (* Vincenzo Librandi, Jul 04 2017 *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 8, 33, 98, 238}, 40] (* Harvey P. Dale, Jun 01 2018 *) PROG (PARI) a(n)=n*(n+1)*(n+2)*(n+3)*(3*n+2)/120 \\ Charles R Greathouse IV, Oct 07 2015 (MAGMA) [0] cat [Binomial(n+4, n)*(3*n+5)/5: n in [0..40]]; // Vincenzo Librandi, Jul 04 2017 CROSSREFS Partial sums of A001296. Cf. A093560 ((3, 1) Pascal, column m=5). Sequence in context: A316148 A014820 A070736 * A278670 A301771 A070051 Adjacent sequences:  A051833 A051834 A051835 * A051837 A051838 A051839 KEYWORD nonn,easy AUTHOR Barry E. Williams, Dec 12 1999 EXTENSIONS Simpler definition from Ben Creech (mathroxmysox(AT)yahoo.com), Nov 13 2005 STATUS approved

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Last modified January 20 16:46 EST 2019. Contains 319335 sequences. (Running on oeis4.)