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A121572 Subprimorials: inverse binomial transform of primorials (A002110). 4
1, 1, 3, 17, 119, 1509, 18799, 342397, 6340263, 151918421, 4619754311, 140219120601, 5396354613583, 221721908976697, 9431597787000999, 447473598316521449, 24163152239530299719, 1444153946379288324477, 87200644323074509092943, 5929294512595059362045041 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Mar 13 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A002110, A000166, A136104.

See A079266 for a different definition of subprimorial.

Sequence in context: A074554 A074544 A165976 * A249924 A074543 A216314

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

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Last modified August 19 21:13 EDT 2017. Contains 290821 sequences.