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%I #11 Feb 27 2019 01:18:38
%S 363,481,3349,2761,25961,22727,263111,237371,21635,8837,695089,529331,
%T 9407549,679829,641069,6671911,36404897,4075097,2159257,1312139,
%U 36516143,35036093,88771727,3715069
%N Numerator of h(n+7) - h(n), where h(n) = Sum_{k=1..n} 1/k.
%C a(n) = numerator(7*n^6 + 168*n^5 + 1610*n^4 + 7840*n^3 + 2037*n^2 + 26264*n + 13068)/((n+1)*n+2)*...*(n+7));
%C (7*n^6 + 168*n^5 + 1610*n^4 + 7840*n^3 + 2037*n^2 + 26264*n + 13068)/a(n) can be factored into 2^m(n)*3^p(n)*5^(q1(n) + q2(n)) where
%C m(n) is of period 4, repeating [2,4,3,4]
%C p(n) is of period 9, repeating [2,2,2,1,1,2,1,1,2]
%C q1(n) is of period 5, repeating [0,0,0,1,1]
%C q2(n) is of period 25, repeating [0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
%F a(n) = (7*n^6 + 168*n^5 + 1610*n^4 + 7840*n^3 + 2037*n^2 + 26264*n + 13068)/ (2^m(n)*3^p(n)*5^(q(n)) where
%F m(n) = P(1,4,3,n) + 2*P(0,2,1,n) + 2,
%F p(n) = P(0,3,2,n) + P(7,9,7,n) + 1,
%F q(n) = P(0,5,3,n) + P(15,15,23,n),
%F P(x,y,z,n) = floor(((n+x) mod y)/z).
%p h:= n-> sum(1/k,k=1..n):seq(numer(h(n+7)-h(n)), n=0..23);
%p P:=(x,y,z,n)-> floor(((n+x) mod y)/z):
%p m:=n-> P(1,4,3,n)+2*P(0,2,1,n)+2:
%p p:=n-> P(0,3,2,n)+P(7,9,7,n)+1:
%p q:=n-> P(0,5,3,n)+P(15,15,23,n):
%p N7:=n->(7*n^6+168*n^5+1610*n^4+7840*n^3+2037*n^2+26264*n+13068): seq(N7(n)/(2^m(n)*3^p(n)*5^q(n)), n=0..23);
%p # Alternative implementation, _R. J. Mathar_, Jul 12 2011:
%p A192449 := proc(n) add(1/i,i=n+1..n+7) ; numer(%) ; end proc:
%Y Cf. A188386, A189642, A189998, A192359.
%K nonn
%O 0,1
%A _Gary Detlefs_, Jul 01 2011
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