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A182016 Central coefficients of triangle A182013. 1
1, 3, 15, 85, 531, 3545, 24833, 180251, 1344163, 10237001, 79287469, 622596063, 4945078477, 39658283943, 320689293119, 2611817435525, 21405148148051, 176396318594937, 1460795339822349, 12150467810552223, 101463416752305385, 850306144532133787 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = sum(M(i),i=n..2*n), where the M(n)'s are the Motzkin numbers.

Recurrence: a(n+1) = a(n) + M(2n+2) + M(2n+1) - M(n).

MATHEMATICA

M[n_]:=If[n==0, 1, Coefficient[(1+x+x^2)^(n+1), x^n]/(n+1)]; Table[Sum[M[i], {i, n, 2n}], {n, 0, 40}]

PROG

(Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)), x^n)/(n+1);

makelist(sum(M(i), i, n, 2*n), n, 0, 20);

CROSSREFS

Sequence in context: A118342 A084209 A317133 * A127085 A326275 A093615

Adjacent sequences:  A182013 A182014 A182015 * A182017 A182018 A182019

KEYWORD

nonn

AUTHOR

Emanuele Munarini, Apr 06 2012

STATUS

approved

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Last modified September 22 07:34 EDT 2020. Contains 337289 sequences. (Running on oeis4.)