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A374488
Expansion of 1/(1 - 2*x - 11*x^2)^(3/2).
1
1, 3, 24, 100, 555, 2541, 12628, 59004, 281655, 1315765, 6171132, 28692456, 133315273, 616780815, 2848833120, 13124483344, 60364983987, 277142478921, 1270586298520, 5817063737100, 26600252408961, 121501917998263, 554429553154044, 2527595449990500
OFFSET
0,2
FORMULA
a(0) = 1, a(1) = 3; a(n) = ((2*n+1)*a(n-1) + 11*(n+1)*a(n-2))/n.
a(n) = binomial(n+2,2) * A025237(n).
PROG
(PARI) a(n) = binomial(n+2, 2)*sum(k=0, n\2, 3^k*binomial(n, 2*k)*binomial(2*k, k)/(k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 09 2024
STATUS
approved