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A034015 a(n) = A027307(n+1)/2. 5
1, 5, 33, 249, 2033, 17485, 156033, 1431281, 13412193, 127840085, 1235575201, 12080678505, 119276490193, 1187542872989, 11909326179841, 120191310803937, 1219780566014657, 12440630635406245, 127446349676475425, 1310820823328281561, 13530833791486094769 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Series reversion of x(Sum_{k>=0} a(k)(-x^2)^k) is Sum_{k odd} C(k)x^k where C() is Catalan numbers A000108.

Series reversion of x(Sum_{k>=0} a(k)(-x)^k) is A000337(x). (Michael Somos)

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014.

FORMULA

a(n) = Sum_{i=0..n} Sum_{j=0..i} (-2)^(n-i)*binomial(i,j)*binomial(2i+j, n)*binomial(n+1,i)/(n+1) (conjectured). - Michael D. Weiner, May 25 2017

MAPLE

a:= proc(n) option remember; `if`(n<2, 4*n+1,

      ((110*n^3+66*n^2-17*n-9) *a(n-1)

       +(n-1)*(2*n-1)*(5*n+3) *a(n-2)) /

      ((2*n+3)*(5*n-2)*(n+1)))

    end:

seq(a(n), n=0..25);  # Alois P. Heinz, Jun 22 2014

MATHEMATICA

a[n_] := If[n<0, 0, Sum[2^i*Binomial[2*n+2, i]*Binomial[n+1, i+1]/(n+1), {i, 0, n}]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Oct 13 2014, after PARI *)

PROG

(PARI) a(n)=if(n<0, 0, sum(i=0, n, 2^i*binomial(2*n+2, i)*binomial(n+1, i+1))/(n+1))

CROSSREFS

Cf. A001003 (part of a family indexed by m: m=1, m=2 this sequence).

Sequence in context: A084771 A153398 A242522 * A268563 A056159 A171804

Adjacent sequences:  A034012 A034013 A034014 * A034016 A034017 A034018

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)