A187756 a(n) = n^2 * (4*n^2 - 1) / 3.
0, 1, 20, 105, 336, 825, 1716, 3185, 5440, 8721, 13300, 19481, 27600, 38025, 51156, 67425, 87296, 111265, 139860, 173641, 213200, 259161, 312180, 372945, 442176, 520625, 609076, 708345, 819280, 942761, 1079700, 1231041, 1397760, 1580865, 1781396, 2000425
Offset: 0
Examples
G.f. = x + 20*x^2 + 105*x^3 + 336*x^4 + 825*x^5 + 1716*x^6 + 3185*x^7 + ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- P. Aluffi, Degrees of projections of rank loci, arXiv:1408.1702 [math.AG], 2014. ["After compiling the results of many explicit computations, we noticed that many of the numbers d_{n,r,S} appear in the existing literature in contexts far removed from the enumerative geometry of rank conditions; we owe this surprising (to us) observation to perusal of [Slo14]."]
- Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
Programs
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Magma
[n^2*(4*n^2-1)/3: n in [0..50]]; // G. C. Greubel, Aug 10 2018
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Mathematica
LinearRecurrence[{5,-10,10,-5,1},{0,1,20,105,336},40] (* Harvey P. Dale, Mar 26 2016 *) a[ n_] := SeriesCoefficient[ x * (1 + x) * (1 + 14*x + x^2) / (1 - x)^5, {x, 0, Abs[n]}]; (* Michael Somos, Dec 26 2016 *) -
Maxima
A187756(n):=n^2*(4*n^2-1)/3$ makelist(A187756(n),n,0,20); /* Martin Ettl, Jan 07 2013 */
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PARI
{a(n) = polcoeff( x * (1 + x) * (1 + 14*x + x^2) / (1 - x)^5 + x * O(x^n), abs(n))};