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

0,1

Comments

This sequence appears in the 5-section of A234042.

Links

Table of n, a(n) for n=0..33.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A113134 A334722 A092818 * A041087 A041084 A115066

Adjacent sequences: A238469 A238470 A238471 * A238473 A238474 A238475

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 28 2014

Status

approved