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A030016 Inverse binomial transform of {1, primes}. 3

%I

%S 1,1,0,1,-2,5,-14,37,-90,205,-442,899,-1700,2913,-4302,4747,-1080,

%T -14001,55336,-150395,346164,-716967,1369430,-2432789,4002994,

%U -5964749,7525018,-6123027,-4900092,40900519,-134308944,348584679,-798958750

%N Inverse binomial transform of {1, primes}.

%H Alois P. Heinz, <a href="/A030016/b030016.txt">Table of n, a(n) for n = 0..1000</a>

%H Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties </a>, arXiv:1103.2582 [math.CO], 2011-2013.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) = A008578(n+1) - sum(k=1..n, C(n,k-1)*a(k-1)). - _Vladimir Kruchinin_, Mar 05 2011

%p b:= n-> `if`(n=1, 1, ithprime(n-1)):

%p a:= proc(n) option remember;

%p b(n+1) -add(binomial(n, k-1) *a(k-1), k=1..n)

%p end:

%p seq(a(n), n=0..35); # _Alois P. Heinz_, Mar 06 2011

%t b[n_] := If[n == 1, 1, Prime[n - 1]]; a[n_] := a[n] = b[n + 1] - Sum [Binomial[n, k - 1]*a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 35}] (* _Jean-Fran├žois Alcover_, Mar 20 2014, after _Alois P. Heinz_ *)

%K sign

%O 0,5

%A _N. J. A. Sloane_.

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Last modified November 13 17:34 EST 2019. Contains 329106 sequences. (Running on oeis4.)