

A134432


Sum of entries in all the arrangements of the set {1,2,...,n} (to n=0 there corresponds the empty set).


4



0, 1, 9, 66, 490, 3915, 34251, 328804, 3452436, 39456405, 488273005, 6510306726, 93097386174, 1421850988831, 23105078568495, 398118276872520, 7251440043035176, 139227648826275369, 2810658160680434001, 59519819873232720010, 1319356007189991960210
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OFFSET

0,3


COMMENTS

a(n) = Sum_{k=0..n(n+1)/2} k*A134431(n,k).
Appears to be the binomial transform of A001286 (filled with the appropriate two leading zeros), shifted one index left.  R. J. Mathar, Apr 04 2012


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..447


FORMULA

a(n) = (d/dt)P[n](t) evaluated at t=1; here P[n](t)=Q[n](t,1) where the polynomials Q[n](t,x) are defined by Q[0]=1 and Q[n]=Q[n1] + xt^n (d/dx)xQ[n1]. (Q[n](t,x) is the bivariate generating polynomial of the arrangements of {1,2,...,n}, where t (x) marks the sum (number) of the entries; for example, Q[2](t,x) = 1 + tx + t^2*x + 2t^3*x^2, corresponding to: empty, 1, 2, 12 and 21, respectively.)


EXAMPLE

a(2)=9 because the arrangements of {1,2} are (empty), 1, 2, 12 and 21.


MAPLE

Q[0]:=1: for n to 17 do Q[n]:=sort(simplify(Q[n1]+t^n*x*(diff(x*Q[n1], x))), t) end do: for n from 0 to 17 do P[n]:=sort(subs(x=1, Q[n])) end do: seq(subs(t =1, diff(P[n], t)), n=0..17);


CROSSREFS

Cf. A000522, A134431.
Sequence in context: A055148 A014830 A048439 * A098107 A226201 A091647
Adjacent sequences: A134429 A134430 A134431 * A134433 A134434 A134435


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Nov 16 2007


EXTENSIONS

More terms from Alois P. Heinz, Dec 22 2017


STATUS

approved



