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A234042
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a(n) = binomial(n+4,4)*gcd(n,5)/5.
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6
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1, 1, 3, 7, 14, 126, 42, 66, 99, 143, 1001, 273, 364, 476, 612, 3876, 969, 1197, 1463, 1771, 10626, 2530, 2990, 3510, 4095, 23751, 5481, 6293, 7192, 8184, 46376, 10472, 11781, 13209, 14763, 82251, 18278, 20254, 22386, 24682, 135751, 29799, 32637, 35673, 38916
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OFFSET
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0,3
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COMMENTS
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The sixth column of the triangle A107711.
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LINKS
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FORMULA
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a(n) = A107711(n+5,5) = binomial(n+5,5)*gcd(n,5)/(n+5), with n >= 0.
O.g.f.: ((1+x^20) + x*(1+x^18) + 3*x^2*(1+x^16) + 7*x^3*(1+x^14) + 14*x^4*(1+x^12) + 121*x^5*(1+x^10)+37*x^6*(1+x^8) + 51*x^7*(1+x^6) + 64*x^8*(1+x^4) + 73*x^9*(1+x^2) + 381*x^10)/(1-x^5)^5. From the 5-section using n = 5*k + j, for j = 0, 1, 2, 3, 4.
Sum_{n>=0} 1/a(n) = 20/3 - 16*sqrt(10-22/sqrt(5))*Pi/5. - Amiram Eldar, Sep 20 2022
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MATHEMATICA
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a[n_] := Binomial[n + 4, 4] * GCD[n, 5]/5; Table[a[n], {n, 0, 40}] (* Amiram Eldar, Sep 20 2022 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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