A131658 - cp's OEIS frontend

A131658 For n >= 1, put A_n(z) = Sum_{j>=0} (nj)!/(j!^n) z^j and B_n(z) = Sum_{j>=0} (nj)!/(j!^n) z^j * (Sum__{k=j+1..jn} (1/k)), and let u(n) be the largest integer for which exp(B_n(z)/(u(n)A_n(z))) has integral coefficients. The sequence is u(n).

n	a(n)
1	1
2	1
3	1
4	2
5	2
6	36
7	36
8	144
9	144
10	1440
11	1440
12	17280
13	17280
14	241920
15	3628800
16	29030400
17	29030400
18	1567641600
19	1567641600
20	156764160000
21	49380710400000
22	217275125760000
23	1086375628800000
24	1738201006080000

[1, 1, 1, 2, 2, 36, 36, 144, 144, 1440, 1440, 17280, 17280, 241920, 3628800, 29030400, 29030400, 1567641600, 1567641600, 156764160000, 49380710400000, 217275125760000, 1086375628800000, 1738201006080000]

cp's OEIS Frontend

A131658 For n >= 1, put A_n(z) = Sum_{j>=0} (nj)!/(j!^n) z^j and B_n(z) = Sum_{j>=0} (nj)!/(j!^n) z^j * (Sum__{k=j+1..jn} (1/k)), and let u(n) be the largest integer for which exp(B_n(z)/(u(n)A_n(z))) has integral coefficients. The sequence is u(n).

Table of values

List of values

cp's OEIS Frontend

A131658 For n >= 1, put A_n(z) = Sum_{j>=0} (n*j)!/(j!^n) * z^j and B_n(z) = Sum_{j>=0} (n*j)!/(j!^n) * z^j * (Sum__{k=j+1..j*n} (1/k)), and let u(n) be the largest integer for which exp(B_n(z)/(u(n)*A_n(z))) has integral coefficients. The sequence is u(n).

Table of values

List of values

A131658 For n >= 1, put A_n(z) = Sum_{j>=0} (nj)!/(j!^n) z^j and B_n(z) = Sum_{j>=0} (nj)!/(j!^n) z^j * (Sum__{k=j+1..jn} (1/k)), and let u(n) be the largest integer for which exp(B_n(z)/(u(n)A_n(z))) has integral coefficients. The sequence is u(n).