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 A343349 Expansion of Product_{k>=1} 1 / (1 - x^k)^(4^(k-1)). 7
 1, 1, 5, 21, 95, 415, 1851, 8155, 36030, 158510, 696502, 3052966, 13359230, 58346206, 254405630, 1107479694, 4813850699, 20894227355, 90567536543, 392066476815, 1695180397145, 7320927664713, 31581573600685, 136094434672509, 585876330191950, 2519701493092958 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) ~ exp(sqrt(n) - 1/8 + c/4) * 2^(2*n - 3/2) / (sqrt(Pi)*n^(3/4)), where c = Sum_{j>=2} 1/(j * (4^(j-1) - 1)). - Vaclav Kotesovec, Apr 12 2021 MAPLE a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add( d*4^(d-1), d=numtheory[divisors](j)), j=1..n)/n) end: seq(a(n), n=0..25); # Alois P. Heinz, Apr 12 2021 MATHEMATICA nmax = 25; CoefficientList[Series[Product[1/(1 - x^k)^(4^(k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[d 4^(d - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 25}] CROSSREFS Cf. A034691, A104460, A144068, A343350, A343351, A343352, A343353, A343354, A343355. Sequence in context: A103519 A178876 A202513 * A159289 A201869 A017968 Adjacent sequences: A343346 A343347 A343348 * A343350 A343351 A343352 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 12 2021 STATUS approved

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Last modified March 24 07:05 EDT 2023. Contains 361454 sequences. (Running on oeis4.)