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 A334370 Expansion of e.g.f. Product_{k>=1} (1 + x^prime(k) / prime(k)!). 1
 1, 0, 1, 1, 0, 11, 0, 22, 56, 36, 2640, 1, 8712, 79, 72436, 360465, 48608, 49008961, 794376, 4232764, 7753140, 942565890, 18198334, 14799637777, 10577976, 366619314900, 2785137222400, 1475339135400, 1065920156634060, 3765722000041, 5869315258699050 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS MATHEMATICA nmax = 30; CoefficientList[Series[Product[(1 + x^Prime[k]/Prime[k]!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[DivisorSum[k, -#/(-#!)^(k/#) &, PrimeQ[#] &] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 30}] PROG (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, 1+isprime(k)*x^k/k!))) \\ Seiichi Manyama, Feb 27 2022 CROSSREFS Cf. A007837, A032310, A115278, A190476, A319113. Sequence in context: A299780 A297873 A298136 * A274851 A075360 A256756 Adjacent sequences: A334367 A334368 A334369 * A334371 A334372 A334373 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 11 2020 STATUS approved

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Last modified February 3 17:00 EST 2023. Contains 360044 sequences. (Running on oeis4.)