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A107587 Expansion of (sqrt(1-2x+5x^2)-sqrt(1-2x-3x^2))/(4x^2). 0
1, 1, 1, 1, 3, 11, 31, 71, 155, 379, 1051, 2971, 8053, 21165, 56057, 152881, 425491, 1186227, 3287971, 9102787, 25346457, 71111377, 200425149, 565676629, 1597672277, 4520632981, 12827046181, 36493762501, 104027787451 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Binomial transform of 1,0,0,0,2,0,0,0,4,.... (see A048990).

LINKS

Table of n, a(n) for n=0..28.

FORMULA

a(n)=sum{k=0..floor(n/2), binomial(n, 2k)C(k)mod(k+1, 2)} where C(n) is A000108.

Conjecture: n*(n+2)*a(n) +(-5*n^2-n+3)*a(n-1) +(10*n^2-16*n+3)*a(n-2) +(-10*n^2+34*n-27)*a(n-3) -(11*n-5)*(n-3)*a(n-4) +15*(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Feb 20 2015

Conjecture: n*(n-2)*(n+2)*a(n) -(2*n-1)*(2*n^2-2*n-3)*a(n-1) +3*(n-1)*(2*n^2-4*n+1)*a(n-2) -2*(n-1)*(n-2)*(2*n-3)*a(n-3) -15*(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Feb 20 2015

CROSSREFS

Sequence in context: A071568 A097081 A093406 * A245931 A190590 A241693

Adjacent sequences:  A107584 A107585 A107586 * A107588 A107589 A107590

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 16 2005

STATUS

approved

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Last modified February 28 04:39 EST 2020. Contains 332321 sequences. (Running on oeis4.)