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A108489 Expansion of 1/sqrt(1-2x-5x^2-6x^3+9x^4). 0
1, 1, 4, 13, 37, 130, 427, 1441, 4954, 16987, 58843, 204610, 713893, 2500183, 8778478, 30898309, 108987427, 385136680, 1363252603, 4832572951, 17153677534, 60961916965, 216887253409, 772400234074, 2753261490919, 9822393082513 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In general, sum{k=0..n, C(n-k,k)^2*a^k*b^(n-k)} has expansion 1/sqrt(1-2bx-(2ab-b^2)x^2-2a*b^2*x^3+(ab)^2*x^4).

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n)=sum{k=0..n, C(n-k, k)^2*3^k}

Conjecture: n*a(n) +(-2*n+1)*a(n-1) +5*(-n+1)*a(n-2) +3*(-2*n+3)*a(n-3) +9*(n-2)*a(n-4)=0. - R. J. Mathar, Feb 20 2015

CROSSREFS

Cf. A108484.

Sequence in context: A067633 A091874 A297391 * A155375 A155307 A155344

Adjacent sequences:  A108486 A108487 A108488 * A108490 A108491 A108492

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 04 2005

STATUS

approved

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Last modified July 23 14:36 EDT 2019. Contains 325255 sequences. (Running on oeis4.)