A365012 E.g.f. satisfies A(x) = exp( x*A(x)/(1 - x * A(x)^2) ).
1, 1, 5, 52, 833, 18116, 498907, 16648402, 653034545, 29450331928, 1501456530131, 85398143019014, 5361130115439529, 368227694339818132, 27468201247134068891, 2211469648218676671466, 191131823105565504395873, 17650493961604405811144624
Offset: 0
Keywords
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..348
Programs
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Mathematica
Array[#!*Sum[ (2 # - k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 19, 0] (* Michael De Vlieger, Aug 18 2023 *) -
PARI
a(n) = n!*sum(k=0, n, (2*n-k+1)^(k-1)*binomial(n-1, n-k)/k!);
Formula
a(n) = n! * Sum_{k=0..n} (2*n-k+1)^(k-1) * binomial(n-1,n-k)/k!.