A346426 -id:A346426 - cp's OEIS frontend

A346851 Number of partitions of the (n+5)-multiset {0,...,0,1,2,...,n} with five 0's.

7, 19, 64, 250, 1098, 5317, 28009, 158926, 963913, 6211190, 42309103, 303388298, 2282055551, 17950884133, 147271359890, 1257195981186, 11143814730044, 102376602296871, 973137213352285, 9556384509085448, 96818497703286895, 1010691906511682642

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

Also number of factorizations of 32 * Product_{i=1..n} prime(i+1).

Alois P. Heinz, Table of n, a(n) for n = 0..572

Row n=5 of A346426.

Cf. A346815.

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

Original entry on oeis.org

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

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

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

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

Row n=6 of A346426.

Cf. A346816.

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

A346853 Number of partitions of the (n+7)-multiset {0,...,0,1,2,...,n} with seven 0's.

Original entry on oeis.org

15, 45, 165, 696, 3281, 16972, 95129, 572402, 3670878, 24947043, 178812542, 1346450836, 10615403987, 87372899947, 748880541151, 6669235464674, 61589598614335, 588758112457852, 5816628899785745, 59303810671002372, 623158622145920252, 6740560881383009077

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

Also number of factorizations of 2^7 * Product_{i=1..n} prime(i+1).

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

Row n=7 of A346426.

Cf. A346817.

A346854 Number of partitions of the (n+8)-multiset {0,...,0,1,2,...,n} with eight 0's.

Original entry on oeis.org

22, 67, 254, 1106, 5372, 28582, 164528, 1015356, 6670707, 46393620, 339996570, 2615434647, 21049370938, 176737599452, 1544325166471, 14012688521840, 131775731386953, 1282115365540605, 12885980284689754, 133595285901023405, 1426880352574841614

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

Also number of factorizations of 2^8 * Product_{i=1..n} prime(i+1).

Alois P. Heinz, Table of n, a(n) for n = 0..570

Row n=8 of A346426.

Cf. A346818.

A346855 Number of partitions of the (n+9)-multiset {0,...,0,1,2,...,n} with nine 0's.

Original entry on oeis.org

30, 97, 381, 1711, 8547, 46677, 275375, 1739545, 11685834, 83025806, 621066569, 4872976895, 39974624783, 341902273528, 3041542225849, 28082214612126, 268589416134352, 2656605574961663, 27131852677678804, 285720796755145126, 3098587829401297824

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

Also number of factorizations of 2^9 * Product_{i=1..n} prime(i+1).

Alois P. Heinz, Table of n, a(n) for n = 0..569

Row n=9 of A346426.

Cf. A346819.

A346856 Number of partitions of the (n+10)-multiset {0,...,0,1,2,...,n} with ten 0's.

Original entry on oeis.org

42, 139, 562, 2593, 13285, 74304, 448391, 2894201, 19847703, 143835137, 1096662664, 8764456134, 73189589547, 636885970213, 5761393880423, 54067289148011, 525377389927629, 5277291236749488, 54713982758644746, 584707936871699621, 6432673787847769686

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

Also number of factorizations of 2^10 * Product_{i=1..n} prime(i+1).

Alois P. Heinz, Table of n, a(n) for n = 0..569

Row n=10 of A346426.

Cf. A346820.

A346857 Number of partitions of the (n+4)-multiset {0,...,0,1,2,3,4} with n 0's.

Original entry on oeis.org

15, 52, 135, 296, 592, 1098, 1940, 3281, 5372, 8547, 13285, 20217, 30231, 44477, 64521, 92397, 130805, 183212, 254163, 349437, 476501, 644796, 866357, 1156291, 1533693, 2022351, 2652054, 3459718, 4491201, 5802986, 7464791, 9562004, 12199357, 15504516, 19633156

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

Also number of factorizations of 2^n * Product_{i=1..4} prime(i+1).

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Column k=4 of A346426.

Cf. A346824.

A346858 Number of partitions of the (n+5)-multiset {0,...,0,1,2,...,5} with n 0's.

Original entry on oeis.org

52, 203, 566, 1315, 2752, 5317, 9722, 16972, 28582, 46677, 74304, 115643, 176551, 264909, 391463, 570530, 821244, 1168733, 1646113, 2296362, 3175362, 4354962, 5927481, 8010519, 10753793, 14346412, 19026984, 25094750, 32924339, 42982320, 55848839, 72241875

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

Also number of factorizations of 2^n * Product_{i=1..5} prime(i+1).

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Column k=5 of A346426.

Cf. A346825.

A346859 Number of partitions of the (n+6)-multiset {0,...,0,1,2,...,6} with n 0's.

Original entry on oeis.org

203, 877, 2610, 6393, 13960, 28009, 52902, 95129, 164528, 275375, 448391, 712800, 1109913, 1696713, 2551726, 3781537, 5530232, 7990242, 11417770, 16150412, 22631546, 31438820, 43321938, 59247482, 80457475, 108538460, 145510420, 193932620, 257037132, 338888022

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

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

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Column k=6 of A346426.

Cf. A346826.

A346860 Number of partitions of the (n+7)-multiset {0,...,0,1,2,...,7} with n 0's.

Original entry on oeis.org

877, 4140, 13082, 33645, 76464, 158926, 309546, 572402, 1015356, 1739545, 2894201, 4694575, 7449098, 11591659, 17728306, 26694963, 39636270, 58103409, 84185849, 120673575, 171271389, 240863809, 335857148, 464602342, 637935348, 869840604, 1178289511, 1586269108

Offset: 0

Alois P. Heinz, Aug 06 2021

nonn

Also number of factorizations of 2^n * Product_{i=1..7} prime(i+1).

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Column k=7 of A346426.

Cf. A346827.

cp's OEIS Frontend

A346851 Number of partitions of the (n+5)-multiset {0,...,0,1,2,...,n} with five 0's.

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

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A346853 Number of partitions of the (n+7)-multiset {0,...,0,1,2,...,n} with seven 0's.

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A346854 Number of partitions of the (n+8)-multiset {0,...,0,1,2,...,n} with eight 0's.

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A346855 Number of partitions of the (n+9)-multiset {0,...,0,1,2,...,n} with nine 0's.

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A346856 Number of partitions of the (n+10)-multiset {0,...,0,1,2,...,n} with ten 0's.

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A346857 Number of partitions of the (n+4)-multiset {0,...,0,1,2,3,4} with n 0's.

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A346858 Number of partitions of the (n+5)-multiset {0,...,0,1,2,...,5} with n 0's.

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A346859 Number of partitions of the (n+6)-multiset {0,...,0,1,2,...,6} with n 0's.

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A346860 Number of partitions of the (n+7)-multiset {0,...,0,1,2,...,7} with n 0's.

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