A131657 - cp's OEIS frontend

A131657 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=1..jn} (1/k)), and let b(n) be the largest integer for which exp(B_n(z)/(b(n)A_n(z))) has integral coefficients. The sequence is b(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	783820800000
21	9876142080000
22	651825377280000
23	217275125760000
24	8691005030400000

[1, 1, 1, 2, 2, 36, 36, 144, 144, 1440, 1440, 17280, 17280, 241920, 3628800, 29030400, 29030400, 1567641600, 1567641600, 783820800000, 9876142080000, 651825377280000, 217275125760000, 8691005030400000]

cp's OEIS Frontend

A131657 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=1..jn} (1/k)), and let b(n) be the largest integer for which exp(B_n(z)/(b(n)A_n(z))) has integral coefficients. The sequence is b(n).

Table of values

List of values

cp's OEIS Frontend

A131657 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=1..j*n} (1/k)), and let b(n) be the largest integer for which exp(B_n(z)/(b(n)*A_n(z))) has integral coefficients. The sequence is b(n).

Table of values

List of values

A131657 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=1..jn} (1/k)), and let b(n) be the largest integer for which exp(B_n(z)/(b(n)A_n(z))) has integral coefficients. The sequence is b(n).