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 A291288 a(n) = binomial(n+3, 3)*(1 + binomial(n+2, 3)/4). 3
 1, 5, 20, 70, 210, 546, 1260, 2640, 5115, 9295, 16016, 26390, 41860, 64260, 95880, 139536, 198645, 277305, 380380, 513590, 683606, 898150, 1166100, 1497600, 1904175, 2398851, 2996280, 3712870, 4566920, 5578760, 6770896, 8168160, 9797865, 11689965 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Isaac Ahern, Sam Cook, Affine Symmetry Tensors in Minkowski Space, American Journal of Undergraduate Research, Volume 13 | Issue 3 | August 2016. Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1). FORMULA From Robert Israel, Aug 28 2017: (Start) a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(n^2-n+6)/144. n*a(n) - (2+3*n)*a(n-1) + (8*n-16)*a(n-2) - (12+6*n)*a(n-3) = 0. G.f.: (6*x^2-2*x+1)/(1-x)^7. (End) MAPLE f:=n->binomial(n+3, 3)*(1+binomial(n+2, 3)/4); [seq(f(n), n=0..40)]; MATHEMATICA Table[Binomial[n+3, 3](1+Binomial[n+2, 3]/4), {n, 0, 40}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 5, 20, 70, 210, 546, 1260}, 40] (* Harvey P. Dale, Mar 12 2024 *) CROSSREFS Sequence in context: A270169 A007327 A055403 * A160549 A089094 A080930 Adjacent sequences: A291285 A291286 A291287 * A291289 A291290 A291291 KEYWORD nonn AUTHOR N. J. A. Sloane, Aug 28 2017 STATUS approved

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Last modified September 16 18:48 EDT 2024. Contains 375977 sequences. (Running on oeis4.)