A382517 Expansion of 1/(1 - x/(1 - 9*x)^(5/3)).
1, 1, 16, 211, 2611, 31426, 373099, 4397527, 51623530, 604629688, 7072089076, 82652922457, 965513250832, 11275328397061, 131649767277064, 1536953772789256, 17941954844917198, 209439428952580837, 2444747948094707815, 28536537876362681194, 333091044353156790346
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, 9^(n-k)*binomial(n+2*k/3-1, n-k));
Formula
a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+2*k/3-1,n-k).
D-finite with recurrence (n-1)*(n-2)*a(n) -3*(19*n-37)*(n-2)*a(n-1) +27*(49*n^2-233*n+278)*a(n-2) +2*(-7655*n^2+39732*n-47656)*a(n-3) +3*(25519*n^2-98445*n-28306)*a(n-4) +54*(2552*n^2-69623*n+281314)*a(n-5) +27*(-137799*n^2+1870137*n-6193006)*a(n-6) +177147*(99*n^2-1323*n+4418)*a(n-7) -3188646*(3*n-20)*(3*n-22)*a(n-8)=0. - R. J. Mathar, Apr 02 2025