A191243 Reversion of x-x^2-x^3-x^4-x^5-x^6.

1, 1, 3, 11, 45, 197, 902, 4269, 20717, 102531, 515521, 2625909, 13521776, 70274194, 368131940, 1941801115, 10304601189, 54976677289, 294708283729, 1586565791533, 8574185062861, 46498569928775, 252966168370110, 1380203261726925, 7550534790990360

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..125

Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2011-2013.

Formula

a(n)=sum(k=1..n-1, binomial(n+k-1,n-1)*sum(r=0..k, binomial(k,r)*sum(m=0..r,(sum(j=0..m, binomial(j,-r+n-m-k-j-1)*binomial(m,j)))*binomial(r,m))))/n, n>1, a(1)=1.

Mathematica

a[1] = 1;
a[n_] := Sum[Binomial[n+k-1, n-1] Sum[Binomial[k, r] Sum[Sum[Binomial[j, -r +n-m-k-j-1] Binomial[m, j], {j, 0, m}] Binomial[r, m], {m, 0, r}], {r, 0, k}], {k, 1, n-1}]/n;
Array[a, 25] (* Jean-François Alcover, Aug 08 2018, from Maxima *)

Prog

(Maxima) a(n):=sum(binomial(n+k-1, n-1)*sum(binomial(k, r)*sum((sum(binomial(j, -r+n-m-k-j-1)*binomial(m, j), j, 0, m))*binomial(r, m), m, 0, r), r, 0, k), k, 1, n-1)/n;
(PARI) x='x+O('x^66); Vec(serreverse(x-x^2-x^3-x^4-x^5-x^6)) /* Joerg Arndt, May 28 2011 */

Crossrefs

Sequence in context: A074532 A049186 A049160 * A217888 A146086 A049177

Adjacent sequences: A191240 A191241 A191242 * A191244 A191245 A191246

Keyword

nonn

Author

Vladimir Kruchinin, May 28 2011

Status

approved