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A154596 a(n) = Sum_{j=1..n-1} A142458(n-1, k)*a(n - k), with a(1) = 1. 1
1, 1, 2, 11, 129, 3214, 162491, 16306117, 3231430542, 1254563121783, 953359099059949, 1417753660258148022, 4128222097278496550683, 23571703478682225135264061, 264268834213603744830353397238 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{j=1..n-1} A142458(n-1, k)*a(n-k), with a(1) = 1.
MATHEMATICA
T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k-m+1)*T[n-1, k, m]];
A142458[n_, k_]:= A142458[n, k] = T[n, k, 3];
a[n_]:= a[n]= If[n==1, 1, Sum[A142458[n-1, j]*a[n-j], {j, n-1}]];
Table[a[n], {n, 30}] (* modified by G. C. Greubel, Mar 16 2022 *)
PROG
(Sage)
@CachedFunction
def T(n, k, m):
if (k==1 or k==n): return 1
else: return (m*(n-k)+1)*T(n-1, k-1, m) + (m*k-m+1)*T(n-1, k, m)
def A142458(n, k): return T(n, k, 3)
@CachedFunction
def A154596(n): return 1 if (n==1) else sum( A142458(n-1, j)*A154596(n-j) for j in (1..n-1) )
[A154596(n) for n in (1..30)] # G. C. Greubel, Mar 16 2022
CROSSREFS
Sequence in context: A104087 A208858 A283537 * A337458 A066382 A276030
KEYWORD
nonn
AUTHOR
EXTENSIONS
Offset changed by G. C. Greubel, Mar 16 2022
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)