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A346852 Number of partitions of the (n+6)-multiset {0,...,0,1,2,...,n} with six 0's. 3
11, 30, 105, 426, 1940, 9722, 52902, 309546, 1933171, 12809264, 89613587, 659255660, 5082342477, 40936552022, 343612396821, 2998777788602, 27155414911274, 254692965196866, 2470107851719160, 24734913573251578, 255396574564032443, 2715780007867965824 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 17:26 EST 2022. Contains 350376 sequences. (Running on oeis4.)