A121572 Subprimorials: inverse binomial transform of primorials (A002110).

1, 1, 3, 17, 119, 1509, 18799, 342397, 6340263, 151918421, 4619754311, 140219120601, 5396354613583, 221721908976697, 9431597787000999, 447473598316521449, 24163152239530299719, 1444153946379288324477, 87200644323074509092943, 5929294512595059362045041

Offset

0,3

Comments

By analogy with subfactorials, which are the inverse binomial transform of the factorials.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k) Prime(k)#, where p# is p primorial and Prime(0)# = 1.

A007318^(-1) * A002110. - Gary W. Adamson, Dec 14 2007

Example

a(3) = 30 - 3*6 + 3*2 - 1 = 17.

Maple

b:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*b(n-1)) end:
a:= n-> add(binomial(n, k)*b(k)*(-1)^(n-k), k=0..n):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 19 2016

Mathematica

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 *)

Crossrefs

Cf. A002110, A000166, A136104.

See A079266 for a different definition of subprimorial.

Sequence in context: A165976 A368965 A344553 * A340993 A249924 A305307

Adjacent sequences: A121569 A121570 A121571 * A121573 A121574 A121575

Keyword

nonn

Author

Franklin T. Adams-Watters, Aug 08 2006

Extensions

More terms from R. J. Mathar, Sep 18 2007

Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar

Status

approved