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 A331334 a(n) = n! * [x^n] exp(1 - 1/(2*x + 1))/(2*x + 1). 1
 1, 0, -4, 32, -240, 1792, -11840, 26112, 1589504, -57548800, 1556757504, -39250780160, 973563695104, -24122607992832, 596246557736960, -14477682566889472, 332039052050104320, -6425352382711857152, 53086817854485692416, 4505005802471597015040, -419037805969718712991744 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..20. FORMULA a(n) = 4*(1 - n)*((n - 1)*a(n - 2) + a(n - 1)). a(n) = (-2)^n*Sum_{k=0..n} A331333(n, k)/(-2)^k. a(n)/(-2)^n = n!*LaguerreL(n, 1) = A009940(n). MAPLE gf := exp(1 - 1/(2*x + 1))/(2*x + 1): ser := series(gf, x, 32): seq(n!*coeff(ser, x, n), n=0..20); # Alternative: a := proc(n) option remember; if n < 2 then 1 - n else 4*(1 - n)*((n - 1)*a(n - 2) + a(n - 1)) fi end: seq(a(n), n=0..20); CROSSREFS Cf. A331333, A009940. Sequence in context: A303457 A303451 A301438 * A301779 A370044 A147551 Adjacent sequences: A331331 A331332 A331333 * A331335 A331336 A331337 KEYWORD sign AUTHOR Peter Luschny, Jan 19 2020 STATUS approved

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Last modified March 4 04:40 EST 2024. Contains 370522 sequences. (Running on oeis4.)