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A103914 Negative of column k=9 sequence of array A103728. 2

%I #4 Jun 16 2016 23:27:27

%S 9,203,10767,46061,475793,6668731,13845629,91598867,266769639,

%T 435522233,1078275557,3609658883,10468384561,14540796059,36461681717,

%U 64117563369,83947073543,180056219381,289521339853,564930693271,1283176845407

%N Negative of column k=9 sequence of array A103728.

%C The two a(n) formulas, given below, produce natural numbers for all n>=0.

%F a(n)=-A103728(n+5, 9)=-(1 -(p(n+5)-1)*binomial(p(n+5)-1, 9))/p(n+5), with p(n):=A000040(n) (n-th prime).

%F a(n)= -(1389456 - 2199276*p(n+5) + 1896380*p(n+5)^2 - 993005*p(n+5)^3 + 332598*p(n+5)^4 - 72723*p(n+5)^5 + 10320*p(n+5)^6 - 915*p(n+5)^7 + 46*p(n+5)^8 - p(n+5)^9)/9! = -sum(A103718(k, m)*p(n+5)^m, m=0..9)/9!.

%Y Cf. A103735 (k=8).

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Feb 24 2005

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Last modified July 9 15:49 EDT 2024. Contains 374187 sequences. (Running on oeis4.)