A380613 Expansion of Product_{k>=1} (1 + x^k)^prime(k)#.
1, 2, 7, 42, 291, 2970, 36950, 597100, 11070875, 248103940, 7018494836, 215718595582, 7881561212732, 320881902092122, 13754717161317416, 643588827524430916, 33926485821837232397, 1992916854095359256932, 121393059052727838936847, 8107963745977267426512386, 574571379331620422000295082
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Primorial.
Programs
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Maple
p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(binomial(p(i), j)*b(n-i*j, i-1), j=0..n/i))) end: a:= n-> b(n$2): seq(a(n), n=0..20); # Alois P. Heinz, Jan 28 2025 -
Mathematica
nmax = 20; CoefficientList[Series[Product[(1 + x^k)^Product[Prime[j], {j, 1, k}], {k, 1, nmax}], {x, 0, nmax}], x] primorial[n_] := Product[Prime[j], {j, 1, n}]; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(j/d + 1) d primorial[d], {d, Divisors[j]}] a[n - j], {j, 1, n}]/n]; Table[a[n], {n, 0, 20}]
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