# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a365777 Showing 1-1 of 1 %I A365777 #13 Nov 16 2023 11:51:46 %S A365777 1,3,15,117,1257,17163,284055,5522877,123344817,3111071283, %T A365777 87454712895,2710961144037,91862770847577,3378032307195003, %U A365777 133970268354806535,5699864583381903597,258956671286986317537,12512342291081486212323,640686944845321006836975 %N A365777 Expansion of e.g.f. (exp(2*x) / (2 - exp(2*x)))^(3/4). %F A365777 a(n) = Sum_{k=0..n} (-2)^(n-k) * (Product_{j=0..k-1} (4*j+3)) * Stirling2(n,k). %F A365777 a(0) = 1; a(n) = Sum_{k=1..n} (-2)^k * (1/2 * k/n - 2) * binomial(n,k) * a(n-k). %F A365777 a(0) = 1; a(n) = 3*a(n-1) + Sum_{k=1..n-1} 2^k * binomial(n-1,k) * a(n-k). %o A365777 (PARI) a(n) = sum(k=0, n, (-2)^(n-k)*prod(j=0, k-1, 4*j+3)*stirling(n, k, 2)); %Y A365777 Cf. A124212, A276371. %Y A365777 Cf. A365794. %K A365777 nonn %O A365777 0,2 %A A365777 _Seiichi Manyama_, Nov 16 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE