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A122877 Expansion of (1-2x-3x^2-(1-x)*sqrt(1-2x-7x^2))/(8x^3). 0
0, 1, 2, 7, 20, 65, 206, 679, 2248, 7569, 25690, 88055, 303964, 1056497, 3693158, 12977655, 45813008, 162400609, 577843890, 2063053991, 7388487460, 26535797729, 95552015614, 344897769991, 1247685613272 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform is A071357.

LINKS

Table of n, a(n) for n=0..24.

FORMULA

a(n) = sum{k=0..n, C(n,k)*2^((k-1)/2)C((k-1)/2+1)(1-(-1)^k)/2}, where C(n)=A000108(n).

a(n) = (1/Pi)*Int(x^n*sqrt(-x^2+2x+7)(x-1)/8,x,1-2sqrt(2),1+2sqrt(2)).

a(n) = sum(j=0..n+1, binomial(j,n-j+3)*2^(n-j+2)*binomial(n+1,j))/(n+1). - Vladimir Kruchinin, May 19 2014

Conjecture: (n+3)*a(n) +(-3*n-4)*a(n-1) +(-5*n-1)*a(n-2) +7*(n-2)*a(n-3)=0. - R. J. Mathar, Feb 23 2015

Conjecture: -(n+3)*(n-1)*a(n) +n*(2*n+1)*a(n-1) +7*n*(n-1)*a(n-2)=0. - R. J. Mathar, Feb 23 2015

PROG

(Maxima)

a(n):=sum(binomial(j, n-j+3)*2^(n-j+2)*binomial(n+1, j), j, 0, n+1)/(n+1); /* Vladimir Kruchinin, May 19 2014 */

CROSSREFS

Sequence in context: A000935 A035071 A055891 * A192680 A000150 A115117

Adjacent sequences:  A122874 A122875 A122876 * A122878 A122879 A122880

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 16 2006

STATUS

approved

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Last modified February 17 14:12 EST 2018. Contains 299296 sequences. (Running on oeis4.)