A135413 Number of at most 4-way branching ordered (i.e., plane) trees.
1, 2, 6, 20, 70, 246, 875, 3144, 11385, 41470, 151778, 557712, 2056210, 7602700, 28180050, 104677280, 389571983, 1452293766, 5422187130, 20271296100, 75878518695, 284339792110, 1066585128810, 4004566131000, 15048213795600
Offset: 1
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 250 terms from G. C. Greubel)
Programs
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Maple
A135413 := proc(n) local ogf,i ; ogf := 1 ; for i from 1 to n do ogf := taylor(ogf*(1+x+x^2+x^3+x^4),x=0,n) ; od: coeftayl(ogf,x=0,n-1) ; end: seq(A135413(n),n=1..30) ; # R. J. Mathar, Apr 21 2008
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Mathematica
Join[{1}, Table[Coefficient[(1 + x + x^2 + x^3 + x^4)^n, x,(n - 1)], {n,2,25}]] (* G. C. Greubel, Oct 13 2016 *) -
Maxima
a(n):=sum((-1)^i*binomial(n,i)*binomial(2*n-5*i-2,n-5*i-1),i,0,(n-1)/5); /* Vladimir Kruchinin, Mar 28 2019 */
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PARI
a(n) = polcoef((1+x+x^2+x^3+x^4)^n, n-1, x); \\ Michel Marcus, Mar 28 2019
Formula
a(n) = [ x^(n-1) ] (1+x+x^2+x^3+x^4)^n.
a(n) = Sum_{i=0..floor((n-1)/5)} (-1)^i * C(n,i) * C(2*n-5*i-2,n-5*i-1). - Vladimir Kruchinin, Mar 28 2019
Extensions
More terms from R. J. Mathar, Apr 21 2008
Comments