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A083860
First subdiagonal of generalized Fibonacci array A083856.
3
0, 1, 1, 5, 11, 55, 176, 937, 3781, 21571, 102455, 624493, 3356640, 21752431, 129055681, 884773585, 5696734715, 41129090011, 283908657880, 2149818248341, 15765656131765, 124759995175751, 965186517474191, 7956847444317049, 64577172850366176, 553048437381116275
OFFSET
0,4
FORMULA
a(n) = (((1 + sqrt(4*n + 5))/2)^n - ((1 - sqrt(4*n + 5))/2)^n)/sqrt(4*n + 5).
a(n) = A193376(n-1, n+1) for n >= 2. - R. J. Mathar, Aug 23 2011
a(n) = Sum_{s = 0..floor((n-1)/2)} binomial(n-1-s, s) * (n+1)^s. - Petros Hadjicostas, Dec 25 2019
MAPLE
T := proc(n, k) local v; option remember; if 0 <= n and k = 0 then v := 0; end if; if 0 <= n and k = 1 then v := 1; end if; if 0 <= n and 2 <= k then v := T(n, k - 1) + n*T(n, k - 2); end if; v; end proc;
seq(T(n + 1, n), n = 0 .. 40); # Petros Hadjicostas, Dec 25 2019
MATHEMATICA
T[_, 0] = 0; T[_, 1|2] = 1;
T[n_, k_] := T[n, k] = T[n, k-1] + n T[n, k-2];
a[n_] := T[n+1, n];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Sep 26 2022 *)
CROSSREFS
Sequence in context: A149529 A149530 A149531 * A141496 A192428 A060358
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 06 2003
STATUS
approved