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 A327006 a(n) = A327005(n, n). 8
 1, 0, 1, 2, 6, 24, 105, 510, 2765, 16408, 105210, 724580, 5330149, 41649828, 344120777, 2995027126, 27368953170, 261825429024, 2615385871053, 27216432127818, 294443944669341, 3305528914953420, 38442535155671262, 462431164589185924, 5745587267806107545 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS G. C. Greubel, Table of n, a(n) for n = 1..540 Peter Luschny, The Bell transform. Retoz, Sous-dérangements, Mai 2021. FORMULA a(n) = Sum_{k=1..n} BM[n][k] where BM is the BellMatrix(j -> j mod n) as defined in A264428. Assuming offset = 0: a(n) = n! * [x^n] exp(1 + (x - 1)*exp(x)). - Contributed by C. L. Martin (Retoz), May 16 2021. a(n) = Sum_{j=0..n} binomial(n, j) * (-2)^(n-j) * A005387(j). - G. C. Greubel, Nov 17 2022 MAPLE # BellMatrix is defined in A264428. a := proc(n) BellMatrix(j -> modp(j, n), n): add(i, i in %[n]) end: seq(a(n), n=1..25); # Or, assuming offset = 0: ser := series(exp(1 + (x - 1)*exp(x)), x=0, 25): seq(n!*coeff(ser, x, n), n = 0..24); # Contributed by C. L. Martin (Retoz), May 16 2021. MATHEMATICA With[{m=40}, CoefficientList[Series[Exp[(x-1)*Exp[x] +1], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, Nov 17 2022 *) PROG (Magma) R:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( Exp((x-1)*Exp(x) + 1) ))); // G. C. Greubel, Nov 17 2022 (SageMath) def A327006_list(prec): P. = PowerSeriesRing(QQ, prec) return P( exp((x-1)*exp(x) +1) ).egf_to_ogf().list() A327006_list(40) # G. C. Greubel, Nov 17 2022 CROSSREFS Cf. A005387, A264428, A327005. Sequence in context: A152323 A337770 A171338 * A163824 A356782 A094433 Adjacent sequences: A327003 A327004 A327005 * A327007 A327008 A327009 KEYWORD nonn AUTHOR Peter Luschny, Aug 13 2019 STATUS approved

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Last modified September 13 18:22 EDT 2024. Contains 375910 sequences. (Running on oeis4.)