A359328 - OEIS

%I #35 Feb 01 2024 16:24:09

%S 1,1,1,2,4,12,46,251,1576,11578,94933,875134,8900088,99276703,

%T 1214131109,16107824706,229757728186,3499486564517,56862172844198,

%U 980725126968577,17899265342632635,345197504845310134,7005723403640260805,149261757412790940113,3329108788695272565243

%N Maximal coefficient of x^2*(x^2 + x^3)*(x^2 + x^3 + x^5)*...*(x^2 + x^3 + x^5 + ... + x^prime(n)).

%C Excluding the term 1 from A326178, the exponents of the product x^0*x^2*(x^2 + x^3)*(x^2 + x^3 + x^5)*...*(x^2 + x^3 + x^5 + ... + x^prime(n)) are given by all the other terms of A326178.

%C a(n) is the number of compositions of the terms of the n-th row of A359337 into n prime parts less than or equal to prime(n), with the first part equal to 2, the second part less than or equal to 3, ..., and the n-th part less than or equal to prime(n).

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%t Table[Max[CoefficientList[Product[Sum[x^Prime[i],{i,k}],{k,n}],x]],{n,0,24}]

%o (PARI) a(n) = vecmax(Vec(prod(k=1, n, sum(i=1, k, x^prime(i))))); \\ _Michel Marcus_, Dec 27 2022

%o (Python)

%o from collections import Counter

%o from sympy import prime, primerange

%o def A359328(n):

%o     if n == 0: return 1

%o     c, p = {0:1}, list(primerange(prime(n)+1))

%o     for k in range(1,n+1):

%o         d = Counter()

%o         for j in c:

%o             a = c[j]

%o             for i in p[:k]:

%o                 d[j+i] += a

%o         c = d

%o     return max(c.values()) # _Chai Wah Wu_, Feb 01 2024

%Y Cf. A000040, A326178, A350457.

%Y Cf. A359337 (corresponding exponents), A359338 (minimal corresponding exponent), A359339 (maximal corresponding exponent).

%K nonn

%O 0,4

%A _Stefano Spezia_, Dec 26 2022