A356392 Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k) )^(1/(1-x)).

1, 1, 3, 17, 99, 769, 6877, 70769, 807321, 10366037, 145721531, 2226927405, 36741898267, 651709348653, 12352436747141, 249152882935829, 5320544034698353, 120008265471779529, 2850195632804141203, 71058458112629765449, 1855470903727083981651

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..440

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356389(k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k))^(1/(1-x))))
(PARI) a356389(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1))/k);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356389(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A356393, A356394.

Cf. A168243, A356336, A356389.

Sequence in context: A155610 A001541 A322242 * A330626 A161940 A074565

Adjacent sequences: A356389 A356390 A356391 * A356393 A356394 A356395

Keyword

nonn

Author

Seiichi Manyama, Aug 05 2022

Status

approved