A382432 - OEIS

%I #7 Mar 31 2025 06:48:05

%S 1,2,8,30,114,436,1676,6468,25040,97190,378050,1473254,5750390,

%T 22476090,87958306,344593314,1351330642,5303953012,20834616860,

%U 81900891372,322168053848,1268071841744,4994044075204,19678407053280,77578340524444,305977596195556,1207325722552016,4765772559893268

%N a(n) = A074829(2*n-1, n).

%H Hebert Pérez-Rosés, <a href="https://arxiv.org/abs/2503.17462">Asymptotic Analysis of Central Binomiacci Numbers</a>, arXiv:2503.17462 [math.CO], 2025. See Table 1 and 2 p. 2. See Table 3 p. 9.

%F D-finite with recurrence (-n+2)*a(n) +(9*n-22)*a(n-1) +(-23*n+72)*a(n-2) +(11*n-58)*a(n-3) +2*(2*n-9)*a(n-4)=0. - _R. J. Mathar_, Mar 31 2025

%o (PARI) T(n, k) = if(k==1 || k==n, fibonacci(n), T(n-1, k-1) + T(n-1, k)); \\ A074829

%o a(n) = T(2*n-1, n);

%o lista(nn) = my(m=matrix(2*nn)); for (n=1, 2*nn, for (k=1, n, m[n, k] = if(k==1 || k==n, fibonacci(n), m[n-1, k-1] + m[n-1, k]););); vector(nn, i, m[2*i-1, i]);

%Y Cf. A074829.

%K nonn

%O 1,2

%A _Michel Marcus_, Mar 25 2025