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Sequence is obtained from Catalan numbers (A000108) by taking the factorial of each digit and adding them up.
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%I #18 Jul 09 2023 13:25:41

%S 1,1,2,120,25,26,9,362906,32,41066,369361,86520,40327,367948,5835,

%T 766968,11053,731572,56192,374411,1615,7256,404818,364605,771205,

%U 404861,51385,727600,379721,42643,807308,1091011,495081,807,777014,772751,1578665,410061,108045

%N Sequence is obtained from Catalan numbers (A000108) by taking the factorial of each digit and adding them up.

%C The primes in this sequence are 2, 369361, 379721, 42643, 1008859, 1505873, 2388293, 3289723, .... [Extended by _Robert G. Wilson v_, Sep 30 2009]

%H Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>

%F a(n) = A061602(A000108(n)). - _Alois P. Heinz_, Jul 09 2023

%e The sum of the factorials of each digit of 9694845 = 9! + 6! + 9! + 4! + 8! + 4! + 5! = 766968.

%p a:= n-> add(i!, i=convert(binomial(2*n, n)/(n+1), base, 10)):

%p seq(a(n), n=0..42); # _Alois P. Heinz_, Jul 09 2023

%t f[n_] := Plus @@ (IntegerDigits@ n!); Table[f@ CatalanNumber@ n, {n, 0, 35}] (* _Robert G. Wilson v_, Sep 30 2009 *)

%Y Cf. A000108, A061602.

%K nonn,base

%O 0,3

%A _Parthasarathy Nambi_, Sep 06 2009

%E a(16) onwards added and offset changed from 1 to 0 by _Robert G. Wilson v_, Sep 30 2009