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A244243
Number of partitions of n into 7 parts such that every i-th smallest part (counted with multiplicity) is different from i.
2
1, 7, 22, 48, 88, 140, 207, 291, 389, 508, 646, 809, 995, 1212, 1457, 1742, 2061, 2425, 2833, 3295, 3808, 4386, 5024, 5737, 6522, 7394, 8349, 9406, 10559, 11827, 13208, 14721, 16361, 18153, 20090, 22198, 24472, 26938, 29591, 32462, 35543, 38866, 42427, 46258
OFFSET
35,2
LINKS
FORMULA
Conjectures from Chai Wah Wu, Apr 18 2024: (Start)
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.
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)
CROSSREFS
Column k=7 of A238406.
Sequence in context: A197059 A331229 A299283 * A223833 A014073 A288114
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 23 2014
STATUS
approved