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A241877
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Number of ascent sequences of length n with exactly seven descents.
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2
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262, 45355, 2945144, 115640368, 3310089672, 76098190354, 1488843551061, 25742974021760, 403792980134432, 5855533942758206, 79621493875268300, 1026297720267259815, 12647422247984279889, 150029397902618780880, 1722644140748876548506, 19232187878731653646068
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OFFSET
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12,1
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LINKS
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FORMULA
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G.f.: see Maple program.
Recurrence: a(n) + 1834933472251084800000*a(n-42) - 29890483744407552000000*a(n-41) + 234674273308869918720000*a(n-40) - 1183460488011095998464000*a(n-39) + 4310616672232759649894400*a(n-38) - 12090110137133949555572736*a(n-37) + 27184553419658691145826304*a(n-36) - 50373565574321929969631232*a(n-35) + 78480773039085711009583104*a(n-34) - 104366600043561766882639872*a(n-33) + 119864288120509558700623872*a(n-32) - 120001551815106232058621952*a(n-31) + 105512719130330131388301056*a(n-30) - 81976491762435391083895296*a(n-29) + 56559443885408831033142528*a(n-28) - 34795705814009881313016960*a(n-27) + 19151295749903563509912816*a(n-26) - 9455656062744697462579008*a(n-25) + 4196934270184509793587272*a(n-24) - 1677368435971517310106656*a(n-23) + 604352766672278616765729*a(n-22) - 196445323903680067600818*a(n-21) + 57626984175715546403919*a(n-20) - 15254915763530534131260*a(n-19) + 3642342102661923055475*a(n-18) - 783681290841137732154*a(n-17) + 151735847111641722501*a(n-16) - 26388336799044975888*a(n-15) + 4112001903716894106*a(n-14) - 572369284218905028*a(n-13) + 70895600662640518*a(n-12) - 7777305431924328*a(n-11) + 751228057187814*a(n-10) - 63431687262564*a(n-9) + 4639853686722*a(n-8) - 290658484080*a(n-7) + 15363592789*a(n-6) - 671812362*a(n-5) + 23646363*a(n-4) - 643644*a(n-3) + 12711*a(n-2) - 162*a(n-1). - Fung Lam, May 06 2014
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MAPLE
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gf:= -(17168622184562688000*x^30 -165990345532165324800*x^29 +764265306648034344960*x^28 -2227477724647806173184*x^27 +4607560717763655094272*x^26 -7188029219365307265024*x^25 +8771965813694591513856*x^24 -8569977967582670585472*x^23
+6800372189878230880624*x^22 -4416996852693953991344*x^21 +2351482055430886572808*x^20 -1019029358088416724440*x^19 +351892979022335268927*x^18 -91463393523130541293*x^17 +14605225422499318735*x^16 +581363497155871899*x^15 -1354208397644673655*x^14 +543643959424172265*x^13 -143184185751363124*x^12 +28224011083685669*x^11
-4287423192624419*x^10 +497037468594090*x^9 -41750353408807*x^8 +2131740277605*x^7 -1413256993*x^6 -10610071423*x^5 +985051074*x^4 -46399717*x^3 +1072084*x^2 -2911*x -262) *x^12 / ((9*x-1) *(8*x-1)^2 *(7*x-1)^3 *(6*x-1)^4 *(5*x-1)^5 *(4*x-1)^6 *(x-1)^6 *(3*x-1)^7 *(2*x-1)^8):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=12..30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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