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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..25. 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 Cf. A083856, A083859. Sequence in context: A149529 A149530 A149531 * A141496 A192428 A060358 Adjacent sequences: A083857 A083858 A083859 * A083861 A083862 A083863 KEYWORD easy,nonn AUTHOR Paul Barry, May 06 2003 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)