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A004282
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n*(n+1)^2*(n+2)^2/12.
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2
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0, 3, 24, 100, 300, 735, 1568, 3024, 5400, 9075, 14520, 22308, 33124, 47775, 67200, 92480, 124848, 165699, 216600, 279300, 355740, 448063, 558624, 690000, 845000, 1026675, 1238328, 1483524, 1766100, 2090175
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
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FORMULA
| C(3+n, 2)*C(3+n, 3). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 10 2006
a(n-1) = sum {1 <= x_1, x_2 <= n} x_1*(det V(x_1,x_2))^2 = sum {1 <= i,j <= n} i*(i-j)^2, where V(x_1,x_2) is the Vandermonde matrix of order 2. - Peter Bala (pbala(AT)toucansurf.com), Sep 21 2007
G.f.: x*(3+6*x+x^2)/(1-x)^6. [Colin Barker, Feb 09 2012]
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MAPLE
| [seq(numbperm (n, 2)*numbperm (n, 3)/12, n=2..31)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007
a:=n->sum(sum((n^3-n^2)/12, j=0..n), k=0..n): seq(a(n), n=1..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
a:=n->(sum((numbcomp(n, 4)*numbcomp(n, 2)), j=3..n)):seq(a(n), n=2..39); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
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MATHEMATICA
| Table[n*(n+1)^2*(n+2)^2/12, {n, 0, 40} (* Vincenzo Librandi, Feb 09 2012 *)
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PROG
| (MAGMA) [n*(n+1)^2*(n+2)^2/12: n in [0..50]]; // Vincenzo Librandi, Feb 09 2012
(PARI) binomial(n+3, 2)*binomial(n+3, 3) \\ Charles R Greathouse IV, Feb 09 2012
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CROSSREFS
| Cf. A006542, A107891, A114242.
Sequence in context: A117642 A156832 A092780 * A164938 A050545 A139031
Adjacent sequences: A004279 A004280 A004281 * A004283 A004284 A004285
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KEYWORD
| nonn,easy,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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