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 A213167 a(n) = n! - (n-2)!. 3
 1, 5, 22, 114, 696, 4920, 39600, 357840, 3588480, 39553920, 475372800, 6187104000, 86699289600, 1301447347200, 20835611596800, 354379753728000, 6381450915840000, 121289412980736000, 2426499634470912000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Row sums of A134433 starting from k=3. a(n) = sum( (-1)^k*k*A008276(n,k), k=1..n-1). a(n) = sum( (-1)^k*k*A054654(n,k), k=1..n-2). For n >= 3, a(n) = number whose factorial base representation (A007623) begins with digits {n-1} and {n-2} followed by n-3 zeros. Viewed in that base, this sequence looks like this: 1, 21, 320, 4300, 54000, 650000, 7600000, 87000000, 980000000, A900000000, BA000000000, ... (where "digits" A and B stand for placeholder values 10 and 11 respectively). - Antti Karttunen, May 07 2015 LINKS FORMULA a(n) = n! - (n-2)!. G.f.: (1/G(0) - 1 - x)/x^2 where G(k) = 1 - x/(x - 1/(x - (k+1)/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Dec 13 2012 G.f.: (1+x)/x^2*(1/Q(0)-1), where Q(k)= 1 - 2*k*x - x^2*(k + 1)^2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, May 08 2013 G.f.: 2*Q(0), where Q(k)= 1 - 1/( (k+1)*(k+2) - x*(k+1)^2*(k+2)^2*(k+3)/(x*(k+1)*(k+2)*(k+3) - 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 08 2013 MATHEMATICA Table[n! - (n - 2)!, {n, 2, 20}] PROG (Maxima) A213167(n):=n!-(n-2)!\$ makelist(A213167(n), n, 2, 30); /* Martin Ettl, Nov 03 2012 */ (Scheme) (define (A213167 n) (- (A000142 n) (A000142 (- n 2)))) ;; Antti Karttunen, May 07 2015 CROSSREFS Column 4 of A257503 (apart from initial 1. Equally, row 4 of A257505). Cf. A000142, A007623, A134433. Cf. A008276, A094638, A008275, A130534. Cf. A054654, A048994, A132393. Cf. A067318. Sequence in context: A162271 A164593 A153789 * A005033 A127618 A127619 Adjacent sequences:  A213164 A213165 A213166 * A213168 A213169 A213170 KEYWORD nonn,easy AUTHOR Olivier Gérard, Nov 02 2012 STATUS approved

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Last modified January 25 01:10 EST 2021. Contains 340414 sequences. (Running on oeis4.)