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A023433 Generalized Catalan Numbers. 1
1, 1, 1, 1, 1, 2, 4, 7, 12, 21, 38, 70, 129, 238, 442, 827, 1556, 2939, 5570, 10593, 20214, 38690, 74251, 142844, 275430, 532215, 1030440, 1998733, 3883552, 7557865, 14730670, 28751455, 56192036, 109959882, 215431019, 422541192, 829642870, 1630613418 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

Recurrence: (n+3)*a(n) = (2*n+3)*a(n-1) - n*a(n-2) + (2*n-3)*a(n-3) + (2*n-9)*a(n-5) - (n-6)*a(n-6) - (2*n-15)*a(n-7) - (n-9)*a(n-8). - Vaclav Kotesovec, Aug 25 2014

a(n) ~ c * d^n / n^(3/2), where d = 2.0423505898306085793498312456063... is the root of the equation -1 - 2*d - d^2 + d^3 - 2*d^4 + d^5 = 0, c = 1.36047848416839112694538628599558274531... . - Vaclav Kotesovec, Aug 25 2014

MAPLE

a:= proc(n) option remember;

      `if`(n=0, 1, a(n-1) +add(a(k)*a(n-3-k), k=2..n-3))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, May 08 2011

MATHEMATICA

Clear[ a ]; a[ 0 ]=1; a[ n_Integer ] := a[ n ]=a[ n-1 ]+Sum[ a[ k ]*a[ n-3-k ], {k, 2, n-3} ];

CROSSREFS

Cf. A000108, A001006, A004148, A006318.

Sequence in context: A218600 A000709 A054161 * A190168 A288133 A005126

Adjacent sequences:  A023430 A023431 A023432 * A023434 A023435 A023436

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 14 19:59 EST 2019. Contains 329128 sequences. (Running on oeis4.)