# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a366645 Showing 1-1 of 1 %I A366645 #9 Oct 15 2023 09:26:00 %S A366645 1,0,0,1,4,10,24,67,200,586,1704,5049,15232,46284,141240,433696, %T A366645 1340500,4164830,12993792,40697472,127941300,403561902,1276763096, %U A366645 4050430502,12882398456,41068966204,131211997496,420056152498,1347272602056,4328764460928,13931034024536 %N A366645 G.f. A(x) satisfies A(x) = 1 + x^3 * (A(x) / (1 - x))^4. %F A366645 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,n-3*k) * binomial(4*k,k) / (3*k+1). %o A366645 (PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, n-3*k)*binomial(4*k, k)/(3*k+1)); %Y A366645 Partial sums give A215340. %Y A366645 Cf. A213336, A364410, A366646. %K A366645 nonn %O A366645 0,5 %A A366645 _Seiichi Manyama_, Oct 15 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE