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A187756 a(n) = n^2 * (4*n^2 - 1) / 3. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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]."]
FORMULA
G.f.: x * (1 + x) * (1 + 14*x + x^2) / (1 - x)^5.
a(n) = a(-n) for all n in Z.
a(n) = n * A000447(n).
G.f. A144853(x) = 1 / (1 - a(1)*x / (1 - a(2)*x / (1 - a(3)*x / ... ))).
EXAMPLE
G.f. = x + 20*x^2 + 105*x^3 + 336*x^4 + 825*x^5 + 1716*x^6 + 3185*x^7 + ...
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 *)
PROG
(PARI) {a(n) = polcoeff( x * (1 + x) * (1 + 14*x + x^2) / (1 - x)^5 + x * O(x^n), abs(n))};
(Maxima) A187756(n):=n^2*(4*n^2-1)/3$ makelist(A187756(n), n, 0, 20); /* Martin Ettl, Jan 07 2013 */
(Magma) [n^2*(4*n^2-1)/3: n in [0..50]]; // G. C. Greubel, Aug 10 2018
CROSSREFS
Sequence in context: A063785 A181703 A334419 * A248087 A209547 A278642
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Jan 03 2013
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)