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1, 2, 13, 98, 884, 8712, 92033, 1022450, 11819620, 141052808, 1727897780, 21634496072, 275950213712, 3576314656800, 46995009879033, 625082413914450, 8403885788094500, 114069363868845000, 1561609591376307572
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OFFSET
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0,2
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COMMENTS
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LINKS
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MATHEMATICA
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T[_, 0] = 1; T[n_, k_] := 1/n DivisorSum[n, If[GCD[k, #] == #, EulerPhi[#]*Binomial[n/#, k/#]^2, 0] &];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* A123610 *)
Table[T[2*n, n], {n, 0, 50}] (* A123617 *)
Table[T[2*n + 2, n], {n, 0, 50}] (* A123618 *)
Table[T[2*n + 2, n]/(n+1), {n, 0, 50}] (* A123619 *)
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PROG
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(PARI) {a(n)=if(n==0, 1, (1/(2*(n+1)^2))*sumdiv(2*n+2, d, if(gcd(n, d)==d, eulerphi(d)*binomial((2*n+2)/d, n/d)^2, 0)))}
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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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