A087193 H(p)/p where p runs through the primes and H(k) is the k-th central hexanomial coefficient (A018901).

3, 9, 156, 3431, 2280921, 64092034, 55747783602, 1700642242677, 1657887524047959, 54732141299289779730, 1783584256683646551447, 63884853139612229737722392, 71016623651822742997810429944, 2380864745882038026563515929162, 2701273375177028344436110369387929

Offset: 1

Author

Benoit Cloitre, Oct 19 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..210 (terms 1..100 from Andrew Howroyd)

Crossrefs

Cf. A000040 (primes), A018901 (central hexanomials).

Programs

Mathematica

f[n_] := Max[CoefficientList[Expand[Sum[x^k, {k, 0, 5}]^n], x]]; Table[f[p]/p, {p, Prime[Range[15]]}] (* Amiram Eldar, Apr 25 2025 *)

PARI

\\ here b(n) is A018901.
b(n) = {if(n==0, 1, sum(k=0, 5*n\12, (-1)^k*binomial(n,k)*binomial(n + 5*n\2 - 6*k - 1, n - 1)))}
a(n) = {my(p=prime(n)); b(p)/p} \\ Andrew Howroyd, Jan 08 2020

Formula

a(n) = A018901(prime(n))/prime(n). - Andrew Howroyd, Jan 08 2020

Extensions

Terms a(13) and beyond from Andrew Howroyd, Jan 08 2020