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 A317421 a(n) = Sum_{k=1..n} binomial(n-1,k-1)*prime(k)*n!/k!. 0
 2, 7, 35, 223, 1711, 15283, 155333, 1766819, 22205615, 305275979, 4553222111, 73179347509, 1260129395189, 23135381385341, 450963438488267, 9298480714769813, 202154606388513675, 4620729025472999443, 110759284511324893795, 2777748141259276697671, 72735279236489471934853 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Lah transform of the primes. LINKS Table of n, a(n) for n=1..21. N. J. A. Sloane, Transforms FORMULA E.g.f.: Sum_{k>=1} prime(k)*(x/(1 - x))^k/k!. MATHEMATICA Table[Sum[Binomial[n - 1, k - 1] Prime[k] n!/k!, {k, n}], {n, 21}] nmax = 21; Rest[CoefficientList[Series[Sum[Prime[k] (x/(1 - x))^k/k!, {k, nmax}], {x, 0, nmax}], x] Range[0, nmax]!] PROG (PARI) for(n=1, 30, print1(sum(k=1, n, binomial(n-1, k-1)*prime(k)*n!/k!), ", ")) \\ G. C. Greubel, Jul 28 2018 (Magma) [(&+[Binomial(n-1, k-1)*NthPrime(k)*Factorial(n)/Factorial(k): k in [1..n]]): n in [1..30]]; // G. C. Greubel, Jul 28 2018 CROSSREFS Cf. A000040, A007443. Sequence in context: A080831 A006947 A182224 * A292182 A185054 A014307 Adjacent sequences: A317418 A317419 A317420 * A317422 A317423 A317424 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jul 27 2018 STATUS approved

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Last modified December 5 23:11 EST 2023. Contains 367594 sequences. (Running on oeis4.)