A356564 Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k) )^x.

1, 0, 2, 0, 28, -30, 888, -1260, 51728, -196560, 5293080, -22286880, 710229408, -4851269280, 138348035616, -1091188098000, 36482139114240, -379928382462720, 11812558481332992, -137793570801143040, 4609972759421554560, -67292912045817561600

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k! * A048272(k-1)/(k-1) * 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))^x))
(PARI) a048272(n) = sumdiv(n, d, (-1)^(n/d+1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*a048272(j-1)/(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A356565, A356566.

Cf. A007113, A048272, A338814, A356392.

Sequence in context: A336287 A337074 A156459 * A007218 A092177 A345762

Adjacent sequences: A356561 A356562 A356563 * A356565 A356566 A356567

Keyword

sign

Author

Seiichi Manyama, Aug 12 2022

Status

approved