A238471 -id:A238471 - cp's OEIS frontend

A238472 a(n) = binomial(5*n+7, 4)/5 for n >= 0.

7, 99, 476, 1463, 3510, 7192, 13209, 22386, 35673, 54145, 79002, 111569, 153296, 205758, 270655, 349812, 445179, 558831, 692968, 849915, 1032122, 1242164, 1482741, 1756678, 2066925, 2416557, 2808774, 3246901, 3734388, 4274810, 4871867, 5529384, 6251311, 7041723

Offset: 0

Wolfdieter Lang, Feb 28 2014

This sequence appears in the 5-section of A234042.

Cf. A000332, A001622, A234042, A151989, A234043, A238471, A238473.

a[n_] := Binomial[5*n + 7, 4]/5; Array[a, 40, 0] (* Amiram Eldar, Sep 20 2022 *)

a(n) = binomial(5*n+7, 4)/5 for n >= 0.
a(n) = A234042(5*n+3) for n >= 0.
a(n) = 7*b(n) + 64*b(n-1) + 51*b(n-2) + 3*b(n-3), with b(n) = binomial(n+4,4) = A000332(n) for n >= 0.
O.g.f.: (7 + 64*x + 51*x^2 + 3*x^3)/(1-x)^5.
Sum_{n>=0} 1/a(n) = 2*sqrt(5+2/sqrt(5))*Pi + 10*sqrt(5)*log(phi) + 15*log(5) - 50, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 20 2022

A238473 a(n) = binomial(5*n+8, 4)/5 for n >= 0.

Original entry on oeis.org

14, 143, 612, 1771, 4095, 8184, 14763, 24682, 38916, 58565, 84854, 119133, 162877, 217686, 285285, 367524, 466378, 583947, 722456, 884255, 1071819, 1287748, 1534767, 1815726, 2133600, 2491489, 2892618, 3340337, 3838121, 4389570, 4998409, 5668488, 6403782, 7208391

Offset: 0

Wolfdieter Lang, Feb 28 2014

This sequence appears in the 5-section of A234042.

Cf. A000332, A001622, A234042, A151989, A234043, A238471, A238472.

a[n_] := Binomial[5*n + 8, 4]/5; Array[a, 40, 0] (* Amiram Eldar, Sep 20 2022 *)

a(n) = binomial(5*n+8, 4)/5 = (5*n+8)*(5*n+7)*(5*n+6)*(n+1)/4! for n >= 0.
a(n) = A234042(5*n+2) for n >= 0.
a(n) = 14*b(n) + 73*b(n-1) + 37*b(n-2) + b(n-3), with b(n) = binomial(n+4,4) = A000332(n) for n >= 0.
O.g.f.: (14 + 73*x + 37*x^2 + x^3)/(1-x)^5.
Sum_{n>=0} 1/a(n) = 110/3 - 2*sqrt(25 - 38/sqrt(5))*Pi - 10*sqrt(5)*log(phi) - 5*log(5), where phi is the golden ratio (A001622). - Amiram Eldar, Sep 20 2022

cp's OEIS Frontend

A238472 a(n) = binomial(5*n+7, 4)/5 for n >= 0.

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