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 A162314 Row sums of A162313. 3
 1, 4, 24, 208, 2400, 34624, 599424, 12107008, 279467520, 7257355264, 209403009024, 6646303019008, 230126121738240, 8632047179874304, 348695526455476224, 15091839203924574208, 696733490476660162560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture: for fixed k = 1,2,..., the sequence obtained by reducing a(n) modulo k is eventually periodic with the exact period dividing phi(k), where phi(k) is the Euler totient function A000010. For example, modulo 24 the sequence becomes [1, 4, 0, 16, 0 16, 0, 16, ...] with an apparent period of 2 beginning at a(2). - Peter Bala, Jul 08 2022 LINKS Table of n, a(n) for n=0..16. FORMULA a(n) = 2^n*A000629(n) = 2^n*Sum_{k = 0..n} k!*Stirling2(n+1,k+1). E.g.f.: exp(2*x)/(2-exp(2*x)) = 1 + 4*x + 24*x^2/2! + 208*x^3/3! + .... G.f.: 2/G(0), where G(k) = 1 + 1/(1 - 8*x*(k+1)/(8*x*(k+1) - 1 + 4*x*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 30 2013 From Peter Bala, Jul 08 2022: (Start) a(n) = Sum_{k = 0..n} (-2)^(n+k)*k!*Stirling2(n,k). Conjectural o.g.f. as a continued fraction of Stieltjes type: 1/(1 - 4*x/(1 - 2*x/(1 - 8*x/(1 - 4*x/(1 - ... - 3*n*x/(1 - 2*n*x/(1 - ...))))))). (End) MAPLE #A162314 with(combinat): a:= n -> 2^n*add(k!*Stirling2(n+1, k+1), k = 0..n): seq(a(n), n = 0..16); CROSSREFS Cf. A000629, A162313. Sequence in context: A297218 A010039 A245407 * A323869 A112141 A077555 Adjacent sequences: A162311 A162312 A162313 * A162315 A162316 A162317 KEYWORD easy,nonn AUTHOR Peter Bala, Jul 01 2009 STATUS approved

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Last modified May 29 08:13 EDT 2023. Contains 363029 sequences. (Running on oeis4.)