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A354003
Inverse Stirling transform of A008578 (1 together with the primes).
1
1, 1, -1, 3, -14, 84, -604, 5020, -47144, 492408, -5653004, 70681706, -955450018, 13878511166, -215521103888, 3562431678650, -62439880637498, 1156609714838858, -22575425757129216, 463085375385002432, -9959296414838153618, 224079866356625633070, -5264190202707104532482
OFFSET
1,4
FORMULA
E.g.f.: log(1 + x) + Sum_{k>=2} prime(k-1) * log(1 + x)^k / k!.
a(n) = Sum_{k=1..n} Stirling1(n,k) * A008578(k).
MATHEMATICA
nmax = 23; CoefficientList[Series[Log[1 + x] + Sum[Prime[k - 1] Log[1 + x]^k/k!, {k, 2, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS1[n, k] If[k == 1, 1, Prime[k - 1]], {k, 1, n}], {n, 1, 23}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 13 2022
STATUS
approved