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A300662
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Expansion of 1/(1 - x - Sum_{k>=2} prime(k-1)*x^k).
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7
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1, 1, 3, 8, 22, 59, 160, 429, 1155, 3105, 8354, 22474, 60457, 162636, 437509, 1176941, 3166097, 8517138, 22912002, 61635707, 165806564, 446037175, 1199887133, 3227823181, 8683185454, 23358686444, 62837334885, 169039070970, 454732963567, 1223279724439, 3290751724917
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: 1/(1 - Sum_{k>=1} A008578(k)*x^k).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=1, 1, ithprime(j-1))*a(n-j), j=1..n))
end:
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MATHEMATICA
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nmax = 30; CoefficientList[Series[1/(1 - x - Sum[Prime[k - 1] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
p[1] = 1; p[n_] := p[n] = Prime[n - 1]; a[n_] := a[n] = Sum[p[k] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 30}]
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CROSSREFS
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Cf. A000040, A008578, A023626, A030011, A030012, A030013, A030014, A030015, A030016, A030017, A030018, A292744, A300632.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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