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 A343582 a(n) = (-1)^n*n!*[x^n] exp(-3*x)/(1 - 2*x). 1
 1, 1, 5, -3, 105, -807, 10413, -143595, 2304081, -41453775, 829134549, -18240782931, 437779321785, -11382260772087, 318703306401405, -9561099177693243, 305955173729230497, -10402475906664696735, 374489132640316502949, -14230587040330864850595, 569223481613238080808201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The row polynomials of the rencontres numbers (A008290) evaluated at -1/2 and normalized by (-2)^n. LINKS Table of n, a(n) for n=0..20. FORMULA a(n) = (-2)^n*Sum_{k=0..n} binomial(n, k)*subfactorial(n - k)*(-1/2)^k. a(n) = 6*(n - 1)*a(n - 2) - (2*n - 3)*a(n - 1) for n >= 3. MAPLE egf := exp(-3*x)/(1 - 2*x): ser := series(egf, x, 32): seq((-1)^n*n!*coeff(ser, x, n), n=0..20); MATHEMATICA a[n_] := (-2)^n Sum[Binomial[n, k] Subfactorial[n - k] (-2)^(-k), {k, 0, n}]; Table[a[n], {n, 0, 20}] PROG (Python) def A343582(): a, b, n = 1, 5, 3 yield 1 yield a while True: yield b a, b = b, 6*(n - 1)*a - (2*n - 3)*b n += 1 a = A343582(); print([next(a) for _ in range(21)]) CROSSREFS Cf. A008290, A000166, A000354. Sequence in context: A350213 A255599 A180403 * A267512 A230389 A048885 Adjacent sequences: A343579 A343580 A343581 * A343583 A343584 A343585 KEYWORD sign AUTHOR Peter Luschny, Apr 24 2021 STATUS approved

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Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)