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%I #23 Mar 13 2017 10:42:09
%S 1,1,3,17,119,1509,18799,342397,6340263,151918421,4619754311,
%T 140219120601,5396354613583,221721908976697,9431597787000999,
%U 447473598316521449,24163152239530299719,1444153946379288324477,87200644323074509092943,5929294512595059362045041
%N Subprimorials: inverse binomial transform of primorials (A002110).
%C By analogy with subfactorials, which are the inverse binomial transform of the factorials.
%H Alois P. Heinz, <a href="/A121572/b121572.txt">Table of n, a(n) for n = 0..350</a>
%F a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k) Prime(k)#, where p# is p primorial and Prime(0)# = 1.
%F A007318^(-1) * A002110. - _Gary W. Adamson_, Dec 14 2007
%e a(3) = 30 - 3*6 + 3*2 - 1 = 17.
%p b:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*b(n-1)) end:
%p a:= n-> add(binomial(n,k)*b(k)*(-1)^(n-k), k=0..n):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Sep 19 2016
%t b[n_] := b[n] = If[n==0, 1, Prime[n]*b[n-1]]; a[n_] := Sum[Binomial[n, k]* b[k]*(-1)^(n-k), {k, 0, n}]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Mar 13 2017, after _Alois P. Heinz_ *)
%Y Cf. A002110, A000166, A136104.
%Y See A079266 for a different definition of subprimorial.
%K nonn
%O 0,3
%A _Franklin T. Adams-Watters_, Aug 08 2006
%E More terms from _R. J. Mathar_, Sep 18 2007
%E Edited by _N. J. A. Sloane_, May 15 2008 at the suggestion of _R. J. Mathar_
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