PROG
(MAGMAMagma) [n*(n+1)*(n+2)*(n^2+7*n+32)/120: n in [1..40]]; // Vincenzo Librandi, Jun 15 2011
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(MAGMAMagma) [n*(n+1)*(n+2)*(n^2+7*n+32)/120: n in [1..40]]; // Vincenzo Librandi, Jun 15 2011
<a href="/index/Rec#order_06">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
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(MAGMA) [n*(n+1)*(n+2)*(n^2+7*n+32)/120: n in [1..40]]; // _Vincenzo Librandi, _, Jun 15 2011
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G.f.: x*(x^2-2*x+2) / (x-1)^6. - Colin Barker, Mar 18 2015
a(n) = n*(n+1)*(n+2)*(n^2+7*n+32)/120.
<a href="/index/Rec#order_06">Index to sequences with linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
a(n) = binomial(n+4, n-1)+binomial(n+2, n-1).
Convolution of triangular numbers with triangular numbers + 1, i.e. [1, 3, 6, 10, 15, 21, ...] with [2, 4, 7, 11, 16, 22, ...].
(PARI) Vec(x*(x^2-2*x+2)/(x-1)^6 + O(x^100)) \\ Colin Barker, Mar 18 2015
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Table[(1/120)*n*(n + 1)*(n + 2)*(n^2 + 7*n + 32), {n, 60}] (* From _Vladimir Joseph Stephan Orlovsky, _, Jun 14 2011 *)