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A213549
Principal diagonal of the convolution array A213548.
3
1, 12, 53, 155, 360, 721, 1302, 2178, 3435, 5170, 7491, 10517, 14378, 19215, 25180, 32436, 41157, 51528, 63745, 78015, 94556, 113597, 135378, 160150, 188175, 219726, 255087, 294553, 338430, 387035, 440696, 499752, 564553, 635460
OFFSET
1,2
FORMULA
G.f.: x*(1 + 7*x + 3*x^2)/(1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = (11*n^4 + 14*n^3 + n^2 - 2*n)/24 = n*(n+1)*(11*n^2 + 3*n - 2)/24.
a(n) = Sum_{i=1..n} (n-i+1)*A000217(n+i-1), see A213548. - Bruno Berselli, Oct 05 2016
MATHEMATICA
(See A213548.)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 12, 53, 155, 360}, 40] (* Harvey P. Dale, Nov 20 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 16 2012
STATUS
approved