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%I #7 Apr 18 2024 11:48:01
%S 1,7,22,48,88,140,207,291,389,508,646,809,995,1212,1457,1742,2061,
%T 2425,2833,3295,3808,4386,5024,5737,6522,7394,8349,9406,10559,11827,
%U 13208,14721,16361,18153,20090,22198,24472,26938,29591,32462,35543,38866,42427,46258
%N Number of partitions of n into 7 parts such that every i-th smallest part (counted with multiplicity) is different from i.
%H Alois P. Heinz, <a href="/A244243/b244243.txt">Table of n, a(n) for n = 35..1000</a>
%F Conjectures from _Chai Wah Wu_, Apr 18 2024: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-8) + a(n-10) + a(n-11) + 2*a(n-12) - 2*a(n-16) - a(n-17) - a(n-18) + a(n-20) + a(n-21) + a(n-23) - a(n-26) - a(n-27) + a(n-28) for n > 77.
%F G.f.: x^35*(-x^42 + 2*x^36 + 2*x^35 + 2*x^34 + 2*x^33 + 4*x^32 + x^31 + 2*x^30 - 3*x^29 - 8*x^28 - 14*x^27 - 25*x^26 - 24*x^25 - 16*x^24 + 4*x^23 + 29*x^22 + 50*x^21 + 58*x^20 + 56*x^19 + 28*x^18 - 8*x^17 - 47*x^16 - 75*x^15 - 76*x^14 - 60*x^13 - 28*x^12 + 10*x^11 + 42*x^10 + 55*x^9 + 53*x^8 + 33*x^7 + 14*x^6 - 5*x^5 - 18*x^4 - 19*x^3 - 14*x^2 - 6*x - 1)/(x^28 - x^27 - x^26 + x^23 + x^21 + x^20 - x^18 - x^17 - 2*x^16 + 2*x^12 + x^11 + x^10 - x^8 - x^7 - x^5 + x^2 + x - 1). (End)
%Y Column k=7 of A238406.
%K nonn
%O 35,2
%A _Alois P. Heinz_, Jun 23 2014