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A343661
Sum of numbers of y-multisets of divisors of x for each x >= 1, y >= 0, x + y = n.
4
1, 2, 4, 7, 12, 19, 30, 46, 70, 105, 155, 223, 316, 443, 619, 865, 1210, 1690, 2354, 3263, 4497, 6157, 8368, 11280, 15078, 19989, 26296, 34356, 44626, 57693, 74321, 95503, 122535, 157101, 201377, 258155, 330994, 424398, 544035, 696995, 892104, 1140298, 1455080
OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} binomial(sigma(k) + n - k - 1, n - k).
EXAMPLE
The a(5) = 12 multisets of divisors:
{1,1,1,1} {1,1,1} {1,1} {1} {}
{1,1,2} {1,3} {2}
{1,2,2} {3,3} {4}
{2,2,2}
MATHEMATICA
multchoo[n_, k_]:=Binomial[n+k-1, k];
Table[Sum[multchoo[DivisorSigma[0, k], n-k], {k, n}], {n, 10}]
CROSSREFS
Antidiagonal sums of the array A343658 (or row sums of the triangle).
Dominates A343657.
A000005 counts divisors.
A007318 counts k-sets of elements of {1..n}.
A059481 counts k-multisets of elements of {1..n}.
A343656 counts divisors of powers.
Sequence in context: A100823 A102346 A333148 * A342229 A326080 A287525
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 30 2021
STATUS
approved