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

0,1

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

Prog

(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

Crossrefs

Row n=6 of A346426.

Cf. A346816.

Sequence in context: A303856 A137411 A002755 * A157827 A242276 A196374

Adjacent sequences: A346849 A346850 A346851 * A346853 A346854 A346855

Keyword

nonn

Author

Alois P. Heinz, Aug 06 2021

Status

approved