A374488 Expansion of 1/(1 - 2*x - 11*x^2)^(3/2).

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

Links

Table of n, a(n) for n=0..23.

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

Cf. A102839, A102840, A374487.

Cf. A014432, A025237, A084603.

Sequence in context: A156832 A092780 A004282 * A216725 A334038 A320976

Adjacent sequences: A374485 A374486 A374487 * A374489 A374490 A374491

Keyword

nonn

Author

Seiichi Manyama, Jul 09 2024

Status

approved