A380614 Product_{n>=1} (1 + x^n)^a(n) = Sum_{n>=0} prime(n)# * x^n.
2, 5, 20, 155, 1860, 24970, 444060, 8583935, 202071920, 5992773714, 186947632200, 7001535728810, 288868991951760, 12455290280871150, 587972068547997856, 31327583556949986095, 1856116108295418943020, 113366872636395467452840, 7619343577986975410930880, 541957669076266404650853414
Offset: 1
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(a(i), j)*b(n-i*j, i-1), j=0..n/i))) end: a:= proc(n) option remember; p(n)-b(n, n-1) end: seq(a(n), n=1..20); # Alois P. Heinz, Jan 28 2025 -
Mathematica
primorial[n_] := Product[Prime[j], {j, 1, n}]; b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; a[n_] := a[n] = primorial[n] - b[n, n - 1]; Array[a, 20]
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