A258364
Sum over all partitions lambda of n into 9 distinct parts of Product_{i:lambda} prime(i).
Original entry on oeis.org
223092870, 281291010, 641200560, 1103452350, 2195564910, 3564916950, 6783216270, 11130902406, 20071816324, 33727230365, 53845325737, 85802963866, 137813486551, 211362471237, 328671594863, 499826194085, 762249961621, 1134280917570, 1705626051462, 2476880995049
Offset: 45
-
g:= proc(n, i) option remember; convert(series(`if`(n=0, 1,
`if`(i<1, 0, add(g(n-i*j, i-1)*(ithprime(i)*x)^j
, j=0..min(1, n/i)))), x, 10), polynom)
end:
a:= n-> coeff(g(n$2), x, 9):
seq(a(n), n=45..70);
A258365
Sum over all partitions lambda of n into 10 distinct parts of Product_{i:lambda} prime(i).
Original entry on oeis.org
6469693230, 6915878970, 16974457500, 30110390310, 56648021430, 91846692630, 166537585410, 268444482090, 465147702876, 769400170732, 1299770760139, 1975738341511, 3175348256422, 4843294699465, 7521662925183, 11300032117575, 17213602502741, 25375081790449
Offset: 55
-
g:= proc(n, i) option remember; convert(series(`if`(n=0, 1,
`if`(i<1, 0, add(g(n-i*j, i-1)*(ithprime(i)*x)^j
, j=0..min(1, n/i)))), x, 11), polynom)
end:
a:= n-> coeff(g(n$2), x, 10):
seq(a(n), n=55..75);
A321267
Sum over all partitions lambda of n^2 into n distinct parts of Product_{i:lambda} prime(i).
Original entry on oeis.org
1, 2, 10, 293, 13548, 1004771, 105790662, 15520714599, 2866040940550, 644990031749283, 172565660755190038, 53896353965879336613, 19285636236859395707186, 7803615223621623613355798, 3533604987768479893645954227, 1774407444088569517287486284422
Offset: 0