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 A334385 E.g.f.: Product_{k>=1} (1 + x^(k*(k + 1)/2) / (k*(k + 1)/2)!). 0
 1, 1, 0, 1, 4, 0, 1, 7, 0, 84, 841, 11, 0, 286, 4004, 1, 8024, 136136, 816, 7775256, 155195040, 54265, 1193830, 0, 109832360, 2749077760, 84987760, 296010, 10716746041, 310545275069, 1201800600, 2444026056820, 77016647623040, 0, 14402113079955304, 504073957798435640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS MATHEMATICA nmax = 35; CoefficientList[Series[Product[(1 + x^(k (k + 1)/2)/(k (k + 1)/2)!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[DivisorSum[k, -#/(-#!)^(k/#) &, IntegerQ[Sqrt[8 # + 1]] &] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 35}] CROSSREFS Cf. A007837, A032310, A053614 (positions of 0's), A115278, A205799. Sequence in context: A097898 A154884 A338813 * A201560 A255644 A059678 Adjacent sequences:  A334382 A334383 A334384 * A334386 A334387 A334388 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 11 2020 STATUS approved

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Last modified April 18 19:31 EDT 2021. Contains 343089 sequences. (Running on oeis4.)