A346852 Number of partitions of the (n+6)-multiset {0,...,0,1,2,...,n} with six 0's.

11, 30, 105, 426, 1940, 9722, 52902, 309546, 1933171, 12809264, 89613587, 659255660, 5082342477, 40936552022, 343612396821, 2998777788602, 27155414911274, 254692965196866, 2470107851719160, 24734913573251578, 255396574564032443, 2715780007867965824

Offset: 0

Author

Alois P. Heinz, Aug 06 2021

Keywords

• nonn

Comments

Also number of factorizations of 2^6 * Product_{i=1..n} prime(i+1).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..571

Crossrefs

Row n=6 of A346426.

Cf. A346816.

Programs

Python

from sympy import divisors, isprime, primorial
from functools import cache
@cache
def T(n, m): # after Indranil Ghosh in A001055
    if isprime(n): return 1 if n <= m else 0
    s = sum(T(n//d, d) for d in divisors(n)[1:-1] if d <= m)
    return s + 1 if n <= m else s
def a(n): return (lambda x: T(x, x))(2**5 * primorial(n))
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Nov 30 2021