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Column k=6 sequence of array A103728.
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%I #6 Sep 03 2022 21:25:17

%S 1,191,853,7537,17587,71369,363749,574621,1895149,3744761,5123791,

%T 9167525,19974397,39789335,49243141,89502667,129269281,154098649,

%U 253600309,345942995,535842121,917491105,1180249901,1333475377

%N Column k=6 sequence of array A103728.

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

%F a(n) = A103728(n+4, 6) = (1 +(p(n+4)-1)*binomial(p(n+4)-1, 6))/p(n+4), with p(n) := A000040(n) (n-th prime).

%F a(n) = (2484 - 3388*p(n+4) + 2359*p(n+4)^2 - 910*p(n+4)^3 + 196*p(n+4)^4 - 22*p(n+4)^5 + p(n+4)^6)/6! = (Sum_{m=0..6} A103718(k, m)*p(n+4)^m)/6!.

%Y Cf. A000040, A103718, A103728.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Feb 24 2005