A025271 - OEIS

A025271

a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5.

1, 1, 2, 1, 6, 18, 52, 165, 518, 1646, 5308, 17258, 56604, 187108, 622632, 2084461, 7016134, 23730006, 80610156, 274911614, 940915892, 3230919164, 11127525464, 38429281122, 133052559772, 461740643276, 1605877668824, 5596283069300

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..28.

Filippo Disanto, The size of the biggest Caterpillar subtree in binary rooted planar trees, arXiv preprint arXiv:1202.5668 [math.CO], 2012-2013. See the sequence F-(3).

FORMULA

G.f.: (1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1))) with k=3. - N. J. A. Sloane, Jul 07 2012

Conjecture: n*a(n) +(n+1)*a(n-1) +(n+8)*a(n-2) +42*(-2*n+7)*a(n-3) +16*(n-6)*a(n-4) +80*(n-7)*a(n-5) +336*(n-8)*a(n-6)=0. - R. J. Mathar, Nov 21 2014

Recurrence: n*a(n) = 2*(2*n-3)*a(n-1) - 16*(n-6)*a(n-4). - Vaclav Kotesovec, Jan 25 2015

MAPLE

For a Maple program see A214198.

MATHEMATICA

nmax = 30; aa = ConstantArray[0, nmax]; aa[[1]] = 1; aa[[2]] = 1; aa[[3]] = 2; aa[[4]] = 1; Do[aa[[n]] = Sum[aa[[k]]*aa[[n-k]], {k, 1, n-1}], {n, 5, nmax}]; aa (* Vaclav Kotesovec, Jan 25 2015 *)

PROG

(PARI) default(seriesprecision, 100); Vec((1-sqrt(1-4*x+16*x^4))/2 + O(x^50)) \\ Michel Marcus, Nov 22 2014

CROSSREFS

Sequence in context: A101032 A366356 A365109 * A153804 A239740 A375255

Adjacent sequences: A025268 A025269 A025270 * A025272 A025273 A025274

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved