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

%I A346852 #10 Nov 30 2021 08:41:18
%S A346852 11,30,105,426,1940,9722,52902,309546,1933171,12809264,89613587,
%T A346852 659255660,5082342477,40936552022,343612396821,2998777788602,
%U A346852 27155414911274,254692965196866,2470107851719160,24734913573251578,255396574564032443,2715780007867965824
%N A346852 Number of partitions of the (n+6)-multiset {0,...,0,1,2,...,n} with six 0's.
%C A346852 Also number of factorizations of 2^6 * Product_{i=1..n} prime(i+1).
%H A346852 Alois P. Heinz, <a href="/A346852/b346852.txt">Table of n, a(n) for n = 0..571</a>
%o A346852 (Python)
%o A346852 from sympy import divisors, isprime, primorial
%o A346852 from functools import cache
%o A346852 @cache
%o A346852 def T(n, m): # after Indranil Ghosh in A001055
%o A346852     if isprime(n): return 1 if n <= m else 0
%o A346852     s = sum(T(n//d, d) for d in divisors(n)[1:-1] if d <= m)
%o A346852     return s + 1 if n <= m else s
%o A346852 def a(n): return (lambda x: T(x, x))(2**5 * primorial(n))
%o A346852 print([a(n) for n in range(1, 11)]) # _Michael S. Branicky_, Nov 30 2021
%Y A346852 Row n=6 of A346426.
%Y A346852 Cf. A346816.
%K A346852 nonn
%O A346852 0,1
%A A346852 _Alois P. Heinz_, Aug 06 2021