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A030055
a(n) = binomial(2*n+1, n-5).
5
1, 13, 105, 680, 3876, 20349, 100947, 480700, 2220075, 10015005, 44352165, 193536720, 834451800, 3562467300, 15084504396, 63432274896, 265182149218, 1103068603890, 4568648125690, 18851684897584
OFFSET
5,2
LINKS
FORMULA
G.f.: x^5*2048/((1-sqrt(1-4*x))^11*sqrt(1-4*x))+(-1/x^6+9/x^5-28/x^4+35/x^3-15/x^2+1/x). - Vladimir Kruchinin, Aug 11 2015
From Amiram Eldar, Jan 24 2022: (Start)
Sum_{n>=5} 1/a(n) = 9497/1260 - 32*Pi/(9*sqrt(3)).
Sum_{n>=5} (-1)^(n+1)/a(n) = 9392*log(phi)/(5*sqrt(5)) - 508169/1260, where phi is the golden ratio (A001622). (End)
MAPLE
seq(binomial(2*n+1, n-5), n=5..25); # Muniru A Asiru, Oct 24 2018
MATHEMATICA
Table[Binomial[2*n+1, n-5], {n, 5, 30}] (* G. C. Greubel, Oct 23 2018 *)
PROG
(PARI) vector(30, n, m=n+4; binomial(2*m+1, m-5)) \\ Michel Marcus, Aug 11 2015
(Magma) [Binomial(2*n+1, n-5): n in [5..30]]; // G. C. Greubel, Oct 23 2018
(GAP) List([5..25], n->Binomial(2*n+1, n-5)); # Muniru A Asiru, Oct 24 2018
CROSSREFS
Diagonal 12 of triangle A100257.
Cf. A001622.
Sequence in context: A317427 A320204 A080422 * A155636 A055902 A295249
KEYWORD
nonn
STATUS
approved