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A334370
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Expansion of e.g.f. Product_{k>=1} (1 + x^prime(k) / prime(k)!).
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1
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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
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OFFSET
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0,6
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LINKS
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Table of n, a(n) for n=0..30.
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MATHEMATICA
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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}]
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PROG
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(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
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CROSSREFS
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Cf. A007837, A032310, A115278, A190476, A319113.
Sequence in context: A299780 A297873 A298136 * A274851 A075360 A256756
Adjacent sequences: A334367 A334368 A334369 * A334371 A334372 A334373
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, May 11 2020
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STATUS
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approved
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