# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a372377 Showing 1-1 of 1 %I A372377 #10 Apr 29 2024 09:06:36 %S A372377 1,1,1,4,13,31,91,313,988,3095,10377,35146,117682,400117,1381582, %T A372377 4779997,16599766,58095076,204319835,720756820,2552544940,9074710255, %U A372377 32356325145,115679362789,414701335849,1490297002000,5367227015647,19369656905210,70038419041844 %N A372377 Expansion of (1/x) * Series_Reversion( x * (1+x)^2 / (1+x+x^3)^3 ). %H A372377 Index entries for reversions of series %F A372377 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+3,k) * binomial(n-k+1,n-3*k). %o A372377 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x)^2/(1+x+x^3)^3)/x) %o A372377 (PARI) a(n, s=3, t=3, u=-2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1); %Y A372377 Cf. A372376, A372378. %K A372377 nonn %O A372377 0,4 %A A372377 _Seiichi Manyama_, Apr 29 2024 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE