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A098123 revision #9

A098123

Number of compositions of n with equal number of even and odd parts.

1, 0, 0, 2, 0, 4, 6, 6, 24, 28, 60, 130, 190, 432, 770, 1386, 2856, 5056, 9828, 18918, 34908, 68132, 128502, 244090, 470646, 890628, 1709136, 3271866, 6238986, 11986288, 22925630, 43932906, 84349336, 161625288, 310404768, 596009494

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OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k=floor(n/3)..floor(n/2)} binomial(2*n-4*k, n-2*k)*binomial(n-1-k, 2*n-4*k-1).

Recurrence: n*(2*n-7)*a(n) = 2*(n-2)*(2*n-5)*a(n-2) + 2*(2*n-7)*(2*n-3)*a(n-3) - (n-4)*(2*n-3)*a(n-4). - Vaclav Kotesovec, May 01 2014

a(n) ~ sqrt(c) * d^n / sqrt(Pi*n), where d = 1.94696532812840456026081823863... is the root of the equation 1-4*d-2*d^2+d^4 = 0, c = 0.225563290820392765554898545739... is the root of the equation 43*c^4-18*c^2+8*c-1=0. - Vaclav Kotesovec, May 01 2014

CROSSREFS

Cf. A045931.

Column k=0 of A242498.

Sequence in context: A192134 A322402 A196877 * A066659 A343468 A287846

Adjacent sequences: A098120 A098121 A098122 * A098124 A098125 A098126

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 24 2004

STATUS

editing