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A254635
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Number of perfect matchings in the P_7 X C_{2n} graph.
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0
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6272, 179928, 6422528, 248864088, 9973238912, 405583759128, 16603641077888, 681794737794072, 28036464541430912, 1153675328152653912, 47487681076805107712, 1954983080255585201112, 80488830677377147883648, 3313925147228829031300248, 136444682110846678973251712
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OFFSET
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2,1
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LINKS
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FORMULA
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a(n) = 2*product_{j=1..n} (80 - 98*cos((2*j-1)*Pi/n) + 24*cos(2*(2*j-1)*Pi/n) - 2*cos(3*(2*j-1)*Pi/n)).
G.f.: 8*x^2*(784 - 67669*x + 2453871*x^2 - 50439798*x^3 + 665164698*x^4 - 6023289070*x^5 + 39096248258*x^6 - 187328171158*x^7 + 676655443050*x^8 - 1870967276271*x^9 + 4004062704149*x^10 - 6684136860372*x^11 + 8747997318284*x^12 - 9001233440740*x^13 + 7286680504380*x^14 - 4634602342804*x^15 + 2308061094588*x^16 - 894754403811*x^17 + 267700931657*x^18 - 61077759670*x^19 + 10454781914*x^20 - 1313064750*x^21 + 117311490*x^22 - 7125462*x^23 + 273866*x^24 - 5849*x^25 + 51*x^26)/((1-x)*(1-4*x+x^2)*(1-14*x+34*x^2-14*x^3+x^4)* (1-8*x+16*x^2-8*x^3+x^4) * (1-56*x+672*x^2-2632*x^3+4094*x^4-2632*x^5+672*x^6-56*x^7+x^8)* (1-32*x+288*x^2-928*x^3+1346*x^4-928*x^5+288*x^6-32*x^7+x^8)).
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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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