A182025 a(n) = 31*binomial(2*n,n-4) + Sum_{i=1..n-4} binomial(2*n,n-4-i)*(4+i).

0, 0, 0, 0, 31, 315, 2112, 11830, 60060, 287028, 1317840, 5883768, 25741485, 110921525, 472431960, 1993896450, 8354335080, 34799391000, 144259293600, 595644532560, 2451231964350, 10059146122662, 41181227878560, 168246990214380, 686162857445736, 2794089011606200, 11362424624634720, 46152024284293200, 187266363241782825

Offset

0,5

Links

Table of n, a(n) for n=0..28.

Olivia Beckwith, Victor Luo, Stephen J. Miller, Karen Shen, Nicholas Triantafillou, Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles, arXiv preprint arXiv:1112.3719 [math.PR], 2011-2012.

Olivia Beckwith, Victor Luo, Stephen J. Miller, Karen Shen, Nicholas Triantafillou, Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles, Electronic Journal of Combinatorial Number Theory, Volume 15 (2015) #A21.

Formula

Conjecture: 558*(n-4)*(n+4)*a(n) +7*(-631*n^2+777*n+4600)*a(n-1) +4370*(n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Aug 08 2012

Maple

f:=n->31*binomial(2*n, n-4)+add(binomial(2*n, n-4-i)*(4+i), i=1..n-4);
[seq(f(n), n=0..40)];

Mathematica

Table[31*Binomial[2n, n-4]+Sum[Binomial[2n, n-4-i](4+i), {i, n-4}], {n, 0, 30}] (* Harvey P. Dale, May 24 2016 *)

Prog

(PARI) a(n) = 31*binomial(2*n, n-4) + sum(i=1, n-4, binomial(2*n, n-4-i)*(4+i)); \\ Michel Marcus, Apr 05 2019

Crossrefs

Cf. A182026.

Sequence in context: A221306 A142382 A137318 * A221189 A362493 A029813

Adjacent sequences: A182022 A182023 A182024 * A182026 A182027 A182028

Keyword

nonn

Author

N. J. A. Sloane, Apr 06 2012

Status

approved