A235536 a(n) = binomial(8*n, 2*n) / (6*n + 1).

1, 4, 140, 7084, 420732, 27343888, 1882933364, 134993766600, 9969937491420, 753310723010608, 57956002331347120, 4524678117939182220, 357557785658996609700, 28545588568201512137904, 2298872717007844035521848, 186533392975795702301759056

Offset

0,2

Comments

This is the case l=6, k=2 of binomial((l+k)*n,k*n)/((l*n+1)/gcd(k,l*n+1)), see Theorem 1.1 in Zhi-Wei Sun's paper.

First bisection of A002293.

Also, the sequence is between A002296 and A235535.

Links

Table of n, a(n) for n=0..15.

Zhi-Wei Sun, On Divisibility Of Binomial Coefficients, Journal of the Australian Mathematical Society 93 (2012), p. 189-201.

Formula

a(n) = A124753(6*n).

From Ilya Gutkovskiy, Jun 21 2018: (Start)

G.f.: 6F5(1/8,1/4,3/8,5/8,3/4,7/8; 1/3,1/2,2/3,5/6,7/6; 65536*x/729).

a(n) ~ 2^(16*n-1)/(sqrt(Pi)*3^(6*n+3/2)*n^(3/2)). (End)

Mathematica

Table[Binomial[8 n, 2 n]/(6 n + 1), {n, 0, 20}]

Prog

(Magma) l:=6; k:=2; [Binomial((l+k)*n, k*n)/(l*n+1): n in [0..20]]; /* where l is divisible by all the prime factors of k */

Crossrefs

Cf. similar sequences generated by binomial((l+k)*n,k*n)/(l*n+1), where l is divisible by all the factors of k: A000108 (l=1, k=1), A001764 (l=2, k=1), A002293 (l=3, k=1), A002294 (l=4, k=1), A002295 (l=5, k=1), A002296 (l=6, k=1), A007556 (l=7, k=1), A062994 (l=8, k=1), A059968 (l=9, k=1), A230388 (l=10, k=1), A048990 (l=2, k=2), A235534 (l=4, k=2), this sequence (l=6, k=2), A187357 (l=3, k=3), A235535 (l=6, k=3).

Sequence in context: A055304 A270065 A002917 * A229453 A215606 A119038

Adjacent sequences: A235533 A235534 A235535 * A235537 A235538 A235539

Keyword

nonn,easy

Author

Bruno Berselli, Jan 12 2014

Status

approved