A353406 -id:A353406 - cp's OEIS frontend

A351681 Stirling transform of {1, primes}.

1, 3, 10, 38, 163, 774, 4004, 22315, 132836, 838378, 5574797, 38861142, 282951538, 2146361911, 16931303262, 138694760316, 1178400013929, 10373294706788, 94511288422822, 890334527133081, 8663213736312460, 86975649078035438, 899960154388259079, 9586293761594853220

Offset: 1

Ilya Gutkovskiy, May 07 2022

nonn

Cf. A008578, A307771, A353406.

nmax = 24; CoefficientList[Series[Exp[x] - 1 + Sum[Prime[k - 1] (Exp[x] - 1)^k/k!, {k, 2, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS2[n, k] If[k == 1, 1, Prime[k - 1]], {k, 1, n}], {n, 1, 24}]

E.g.f.: exp(x) - 1 + Sum_{k>=2} prime(k-1) * (exp(x) - 1)^k / k!.

a(n) = Sum_{k=1..n} Stirling2(n,k) * A008578(k).

A354002 Inverse Stirling transform of odd primes.

Original entry on oeis.org

3, 2, -2, 6, -30, 192, -1440, 12240, -115916, 1209422, -13784264, 170426380, -2272355448, 32507854434, -496746974148, 8076163535824, -139211242006108, 2536169979011432, -48695473146705746, 982863502262307532, -20805668315828056010, 460926536131613987430

Offset: 1

Ilya Gutkovskiy, May 13 2022

sign

Winston de Greef, Table of n, a(n) for n = 1..448

Cf. A065091, A307772, A307773, A353406, A354003.

nmax = 22; CoefficientList[Series[Sum[Prime[k + 1] Log[1 + x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS1[n, k] Prime[k + 1], {k, 1, n}], {n, 1, 22}]

a(n) = sum(k=1, n, stirling(n,k,1) * prime(k+1)); \\ Michel Marcus, May 13 2022

E.g.f.: Sum_{k>=1} prime(k+1) * log(1 + x)^k / k!.

a(n) = Sum_{k=1..n} Stirling1(n,k) * prime(k+1).

cp's OEIS Frontend

A351681 Stirling transform of {1, primes}.

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