A233658 7*binomial(4*n + 7, n)/(4*n + 7).
1, 7, 49, 357, 2695, 20930, 166257, 1344904, 11042724, 91801255, 771201431, 6536904290, 55838330730, 480197194260, 4154140621425, 36126361733616, 315647802951628, 2769544822393356, 24392874398953060, 215582307059144025, 1911286446370861455, 16993580092566979770, 151491588134469616215
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.
- Thomas A. Dowling, Catalan Numbers Chapter 7
- Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15: 939-955.
Programs
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Magma
[7*Binomial(4*n+7,n)/(4*n+7): n in [0..30]];
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Mathematica
Table[7 Binomial[4 n + 7, n]/(4 n + 7), {n, 0, 30}] -
PARI
a(n) = 7*binomial(4*n+7,n)/(4*n+7);
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PARI
{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(4/7))^7+x*O(x^n)); polcoeff(B, n)}
Formula
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=4, r=7.
D-finite with recurrence 3*(3*n+5)*(3*n+7)*(n+2)*a(n) -(n+1)*(661*n^2+1301*n+558)*a(n-1) +120*(4*n+1)*(2*n+1)*(4*n-1)*a(n-2)=0. - R. J. Mathar, Nov 22 2024
D-finite with recurrence 3*n*(3*n+5)*(3*n+7)*(n+2)*a(n) -8*(4*n+5)*(2*n+3)*(4*n+3)*(n+1)*a(n-1)=0. - R. J. Mathar, Nov 22 2024
Comments