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A187848 a(n) is the moment of order n for the probability density function defined by rho(x)=exp(x-1)/((Ei(x-1))^2+Pi^2) over the interval 1..infinity, with Ei the exponential integral. 2
1, 4, 20, 120, 836, 6608, 58324, 568296, 6060340, 70245856, 879937892, 11853424536, 170963881892, 2629912684784, 42995842035316, 744683072665416, 13624184625098644, 262594854417561856, 5319099368762699012, 112977659152942035192, 2511041582408699358980 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the binomial transform of A003319(n+1).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

Let c(n)=A000522(n) and An the square matrix of order n+2 defined by: if j<=i A[i,j]=c(i-j+1); A(i,i+1)=1; if j>i+1 A[i,j]=0; then a(n)=(-1)^(n+1)*det(An).

G.f.: (1 - 2*x - U(0))/x^2 where U(k)=  1 - x - x*(k+1)/(1 - x*(k+1)/U(k+1)) ; (continued fraction, 2-step). - Sergei N. Gladkovskii, Oct 14 2012

G.f.: 1/x^2 - 1/x  -1/(x^2*W(0)) , where W(k) = 1 - x*(k+1)/( x*(k+1) - 1/(1 - x*(k+1)/( x*(k+2) - 1/W(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Aug 25 2013

G.f.: W(0)/x - 1/x, where W(k) = 1 - x*(k+1)/( x*(k+2) - 1/(1 - x*(k+1+R)/( x*(k+1+R) - 1/W(k+1) ))); R=1 (continued fraction). - Sergei N. Gladkovskii, Aug 26 2013

a(n) ~ exp(1) * n! * n^2 * (1 - 1/n - 4/n^3 - 23/n^4 - 175/n^5 - 1615/n^6 - 17375/n^7 - 212607/n^8 - 2909007/n^9 - 43953071/n^10). - Vaclav Kotesovec, Sep 02 2014, updated Aug 01 2015

MAPLE

with(LinearAlgebra):

c:= proc(n) option remember; add(n!/k!, k=0..n) end:

a:= n-> (-1)^(n+1) *Determinant(Matrix(n+2,

        (i, j)-> `if`(0<=i+1-j, c(i+1-j), 0))):

seq(a(n), n=0..20);  # Alois P. Heinz, Mar 24 2011

# second Maple program:

b:= proc(n) option remember;

      `if`(n<0, -1, -add(b(n-i)*i!, i=1..n+1))

    end:

a:= n-> add(b(k+1)*binomial(n, k), k=0..n):

seq(a(n), n=0..20);  # Alois P. Heinz, Aug 26 2013

MATHEMATICA

b[n_] := b[n] = If[n<0, -1, -Sum[b[n-i]*i!, {i, 1, n+1}]]; a[n_] := Sum[b[k+1] * Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Jun 30 2015, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A277920 A093123 A092055 * A001715 A304069 A020028

Adjacent sequences:  A187845 A187846 A187847 * A187849 A187850 A187851

KEYWORD

nonn

AUTHOR

Groux Roland, Mar 14 2011

STATUS

approved

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Last modified February 21 23:29 EST 2019. Contains 320381 sequences. (Running on oeis4.)