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A108489 Expansion of 1/sqrt(1-2x-5x^2-6x^3+9x^4). 1
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

Michael De Vlieger, Table of n, a(n) for n = 0..1785

Hacène Belbachir and Abdelghani Mehdaoui, Recurrence relation associated with the sums of square binomial coefficients, Quaestiones Mathematicae (2021) Vol. 44, Issue 5, 615-624.

FORMULA

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

D-finite with recurrence: 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

MATHEMATICA

Array[Sum[Binomial[# - k, k]^2*3^k, {k, 0, #}] &, 26, 0] (* Michael De Vlieger, Sep 10 2021 *)

CROSSREFS

Cf. A108484.

Sequence in context: A067633 A091874 A297391 * A155375 A155307 A155344

Adjacent sequences:  A108486 A108487 A108488 * A108490 A108491 A108492

KEYWORD

easy,nonn,changed

AUTHOR

Paul Barry, Jun 04 2005

STATUS

approved

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Last modified September 19 00:22 EDT 2021. Contains 347549 sequences. (Running on oeis4.)