2,1

Number of big descents in all permutations of [n+1]. A big descent in a permutation (x_1,x_2,...,x_n) is a position i such that x_i - x_(i+1) >= 2. Example: a(2)=2 because there are 2 big descents in the permutations 123, 132, 213, 23\1, 3\12, 321 of {1,2,3} (shown by a \). a(n)=Sum(k*A120434(n+1,k),k=0..n-1) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 01 2006

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Index entries for sequences related to factorial numbers

seq(n!*binomial(n, 2), n=2..20); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 01 2006

a:=n->sum((n-j)*n!, j=1..n): seq(a(n), n=2..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2007

restart: G(x):=x^2/(1-x)^3: f[0]:=G(x): for n from 1 to 18 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=2..16); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 01 2009]

Cf. A120434.

Sequence in context: A073512 A005544 A154636 this_sequence A052640 A037565 A125835

Adjacent sequences: A001801 A001802 A001803 this_sequence A001805 A001806 A001807

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).