A235534 a(n) = binomial(6*n, 2*n) / (4*n + 1).

1, 3, 55, 1428, 43263, 1430715, 50067108, 1822766520, 68328754959, 2619631042665, 102240109897695, 4048514844039120, 162250238001816900, 6568517413771094628, 268225186597703313816, 11034966795189838872624, 456949965738717944767791

Offset

0,2

Comments

This is the case l=4, 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 A001764.

Links

Table of n, a(n) for n=0..16.

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

Formula

a(n) = A047749(4*n-2) for n>0.

From Ilya Gutkovskiy, Jun 21 2018: (Start)

G.f.: 4F3(1/6,1/3,2/3,5/6; 1/2,3/4,5/4; 729*x/16).

a(n) ~ 3^(6*n+1/2)/(sqrt(Pi)*2^(4*n+7/2)*n^(3/2)). (End)

Mathematica

Table[Binomial[6 n, 2 n]/(4 n + 1), {n, 0, 20}]

Prog

(Magma) l:=4; 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), this sequence (l=4, k=2), A235536 (l=6, k=2), A187357 (l=3, k=3), A235535 (l=6, k=3).

Sequence in context: A156379 A119192 A103134 * A300992 A304640 A356483

Adjacent sequences: A235531 A235532 A235533 * A235535 A235536 A235537

Keyword

nonn,easy

Author

Bruno Berselli, Jan 12 2014

Status

approved