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 A356440 Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^(1/(1-x)). 3
 1, 1, 8, 99, 2444, 101450, 7045194, 701736966, 97147459184, 17505366041880, 4005462950166600, 1128394974054308400, 384386423684496873672, 155497732356686080354968, 73718160600338917089657216, 40462026280443230503858113240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..15. FORMULA a(0) = 1; a(n) = Sum_{k=1..n} A356437(k) * binomial(n-1,k-1) * a(n-k). PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(k*x)^k)^(1/k))^(1/(1-x)))) (PARI) a356437(n) = n!*sum(k=1, n, sigma(k, k)/k); a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356437(j)*binomial(i-1, j-1)*v[i-j+1])); v; CROSSREFS Cf. A356437, A356439. Sequence in context: A293145 A305919 A286841 * A367445 A316870 A181034 Adjacent sequences: A356437 A356438 A356439 * A356441 A356442 A356443 KEYWORD nonn AUTHOR Seiichi Manyama, Aug 07 2022 STATUS approved

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Last modified September 14 10:49 EDT 2024. Contains 375921 sequences. (Running on oeis4.)