A346852 - OEIS

%I #10 Nov 30 2021 08:41:18

%S 11,30,105,426,1940,9722,52902,309546,1933171,12809264,89613587,

%T 659255660,5082342477,40936552022,343612396821,2998777788602,

%U 27155414911274,254692965196866,2470107851719160,24734913573251578,255396574564032443,2715780007867965824

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

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

%H Alois P. Heinz, <a href="/A346852/b346852.txt">Table of n, a(n) for n = 0..571</a>

%o (Python)

%o from sympy import divisors, isprime, primorial

%o from functools import cache

%o @cache

%o def T(n, m): # after Indranil Ghosh in A001055

%o     if isprime(n): return 1 if n <= m else 0

%o     s = sum(T(n//d, d) for d in divisors(n)[1:-1] if d <= m)

%o     return s + 1 if n <= m else s

%o def a(n): return (lambda x: T(x, x))(2**5 * primorial(n))

%o print([a(n) for n in range(1, 11)]) # _Michael S. Branicky_, Nov 30 2021

%Y Row n=6 of A346426.

%Y Cf. A346816.

%K nonn

%O 0,1

%A _Alois P. Heinz_, Aug 06 2021