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#20 by Alois P. Heinz at Thu Jun 14 16:18:51 EDT 2018
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#19 by Jean-François Alcover at Thu Jun 14 15:46:32 EDT 2018
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#18 by Jean-François Alcover at Thu Jun 14 15:46:27 EDT 2018
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| MATHEMATICA
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U[n_, k_] := DivisorSum[GCD[n, k], EulerPhi[#]*Binomial[(n+k)/#, n/#]/(n+k) &];
a[1] = 2; a[n_] := 2*Sum[ U[i, n*(10 - i)], {i, 0, 10}];
Array[a, 30] (* Jean-François Alcover, Jun 14 2018, after Andrew Howroyd *)
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| STATUS
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approved
editing
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#17 by Alois P. Heinz at Tue Jan 09 15:46:36 EST 2018
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#16 by Colin Barker at Tue Jan 09 12:48:31 EST 2018
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#15 by Colin Barker at Tue Jan 09 12:44:40 EST 2018
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| FORMULA
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G.f.: 2*x*(1 + 763*x + 905*x^2 + 1871*x^3 + 2142*x^4 + 2318*x^5 + 2333*x^6 + 1022*x^7 + 602*x^8 - 348*x^9 - 1422*x^10 - 1599*x^11 - 2949*x^12 - 3041*x^13 - 2413*x^14 - 2329*x^15 - 316*x^16 - 538*x^17 + 175*x^18 + 703*x^19 + 562*x^20 + 1446*x^21 + 852*x^22 + 147*x^23 + 48*x^24 - 646*x^25 - 6*x^26 + 224*x^27 + 16*x^28 + 184*x^29 - 310*x^30 + 107*x^31) / ((1 - x)^9*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^3*(1 + x^3 + x^6)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) (conjectured). - Colin Barker, Jan 09 2018
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| STATUS
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proposed
editing
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#14 by Andrew Howroyd at Tue Jan 09 11:54:11 EST 2018
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#13 by Andrew Howroyd at Tue Jan 09 11:53:54 EST 2018
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#12 by Andrew Howroyd at Tue Jan 09 11:52:32 EST 2018
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| FORMULA
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a(n) = 2*Sum_{i=0..10} A241926(i, n*(10-i)) for n > 1. - Andrew Howroyd, Jan 09 2018
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| PROG
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(PARI) \\ here U is A241926
U(n, k)={sumdiv(gcd(n, k), d, eulerphi(d)*binomial((n+k)/d, n/d)/(n+k))}
a(n)={2*if(n<2, n==1, sum(i=0, 10, U(i, n*(10-i))))} \\ Andrew Howroyd, Jan 09 2018
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| CROSSREFS
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Cf. A241926, A296360, A296361, A296362.
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| STATUS
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proposed
editing
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#11 by Lars Blomberg at Tue Jan 09 10:59:10 EST 2018
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