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A132364 Expansion of 1/(1-x^2*c(x)), c(x) the g.f. of A000108. 6
1, 0, 1, 1, 3, 7, 20, 59, 184, 593, 1964, 6642, 22845, 79667, 281037, 1001092, 3595865, 13009673, 47366251, 173415176, 638044203, 2357941142, 8748646386, 32576869203, 121701491701, 456012458965, 1713339737086 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Diagonal sums of A106566.
LINKS
Paul Barry, A note on Krawtchouk Polynomials and Riordan Arrays, JIS 11 (2008) 08.2.2.
George Beck and Karl Dilcher, A Matrix Related to Stern Polynomials and the Prouhet-Thue-Morse Sequence, arXiv:2106.10400 [math.CO], 2021.
FORMULA
a(0)=1, a(n) = Sum_{k=0..floor(n/2)} (k/(n-k))*C(2n-3k-1,n-2k)), n>0 .
G.f.: (2-x-x*sqrt(1-4*x))/(2-2*x+2*x^3). - Philippe Deléham, Feb 24 2013
Conjecture: +(-n+1)*a(n) +(5*n-11)*a(n-1) +2*(-2*n+5)*a(n-2) +(-n+1)*a(n-3) +2*(2*n-5)*a(n-4)=0. - R. J. Mathar, Aug 28 2015
a(n) ~ 2^(2*n + 2) / (49 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Nov 13 2022
MATHEMATICA
a[0] := 1; a[n_] := Sum[(k/(n - k))*Binomial[2*n - 3*k - 1, n - 2*k], {k, 0, Floor[n/2]}]; Table[a[n], {n, 0, 25}] (* G. C. Greubel, Oct 19 2016 *)
PROG
(PARI) c(x) = (1 - sqrt(1 - 4*x)) / (2*x); \\ A000108
my(x='x+O('x^30)); Vec(1/(1-x^2*c(x))) \\ Michel Marcus, Nov 13 2022
CROSSREFS
Sequence in context: A129429 A084204 A030238 * A110490 A132868 A357792
KEYWORD
nonn
AUTHOR
Philippe Deléham, Nov 08 2007
EXTENSIONS
Typo in a(n) term corrected Johannes W. Meijer, Sep 13 2010
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)