A378424 Product_{n>=1} (1+x^n)^a(n) = Sum_{k>=0} C(k)*x^k, where C(k) = A000108(k).

1, 2, 3, 10, 25, 78, 245, 810, 2700, 9250, 32065, 112710, 400023, 1432858, 5170575, 18784170, 68635477, 252088416, 930138521, 3446167850, 12815663595, 47820447026, 178987624513, 671825132838, 2528212128750, 9536895064398, 36054433807398, 136583761444354, 518401146543811, 1971076361996550, 7506908923471953, 28634752211620266

Offset

1,2

Comments

Conjecture: A327937(n) divides a(n).

Links

Table of n, a(n) for n=1..32.

Formula

Inverse Euler transform of A179277.

Prog

(PARI)
A179277(n) = if(n<=1, 1, sum(k=0, floor(n/2), A179277(k)*binomial(2*n-4*k, n-2*k)/(n-2*k+1)))
a(max_n) = {my(va, vb, vc); vc=va=vector(max_n); vb = vector(max_n, k, A179277(k)); for(k=1, max_n, vc[k]=k*vb[k]-sum(m=1, k-1, vc[m]*vb[k-m])); for(k=1, max_n, va[k]=1/k*sumdiv(k, m, moebius(k/m)*vc[m])); va; }

Crossrefs

Cf. A000108, A157161, A179277, A327937.

Sequence in context: A103018 A246437 A341265 * A005158 A370608 A182926

Adjacent sequences: A378421 A378422 A378423 * A378425 A378426 A378427

Keyword

nonn,new

Author

Thomas Scheuerle, Nov 26 2024

Status

approved