A382432 a(n) = A074829(2*n-1, n).

1, 2, 8, 30, 114, 436, 1676, 6468, 25040, 97190, 378050, 1473254, 5750390, 22476090, 87958306, 344593314, 1351330642, 5303953012, 20834616860, 81900891372, 322168053848, 1268071841744, 4994044075204, 19678407053280, 77578340524444, 305977596195556, 1207325722552016, 4765772559893268

Offset: 1

Author

Michel Marcus, Mar 25 2025

Keywords

• nonn

Links

• Hebert Pérez-Rosés, Asymptotic Analysis of Central Binomiacci Numbers, arXiv:2503.17462 [math.CO], 2025. See Table 1 and 2 p. 2. See Table 3 p. 9.

Crossrefs

Cf. A074829.

Programs

PARI

T(n, k) = if(k==1 || k==n, fibonacci(n), T(n-1, k-1) + T(n-1, k)); \\ A074829
a(n) = T(2*n-1, n);
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]);

Formula

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