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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 (list; graph; refs; listen; history; text; internal format)
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[n-1] + xt^n (d/dx)xQ[n-1]. (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[n-1]+t^n*x*(diff(x*Q[n-1], 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

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Last modified December 14 09:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)