A306634 Numbers k such that A215339(6*k+2) = 0.

0, 2755452, 4570452, 123725995972

Offset

1,2

Comments

Numbers k such that b(k) is an integer, where b(n) = Sum_{k=0..n} (2*n+k)!/((2*n-2*k)!*(3*k+1)!) (= A001608(6*n+2)/(6*n+2)).

Links

Table of n, a(n) for n=1..4.

Don Zagier, Problems posed at the St Andrews Colloquium, 1996, See "Fifth Day: Sequences and recursions, problem 2".

Example

n |       b(n)
--+--------------------------
0 |       1    (=       2/2)
1 |       5/4  (=      10/8)
2 |      51/14
3 |     277/20
4 |    1497/26
5 |    4045/16 (=    8090/32)
6 |   43721/38
7 |  118141/22 (=  236282/44)
8 |  638471/25 (= 1276942/50)
9 | 6900995/56

Crossrefs

Cf. A001608, A013998, A215339.

Sequence in context: A051384 A251350 A238070 * A015336 A251835 A295471

Adjacent sequences: A306631 A306632 A306633 * A306635 A306636 A306637

Keyword

nonn,more

Author

Seiichi Manyama, Mar 02 2019

Status

approved