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

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..348

Formula

a(n) = n! * Sum_{k=0..n} (2*n-k+1)^(k-1) * binomial(n-1,n-k)/k!.

Mathematica

Array[#!*Sum[ (2 # - k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 19, 0] (* Michael De Vlieger, Aug 18 2023 *)

Prog

(PARI) a(n) = n!*sum(k=0, n, (2*n-k+1)^(k-1)*binomial(n-1, n-k)/k!);

Crossrefs

Cf. A052873, A365013.

Sequence in context: A099881 A280063 A363356 * A367165 A357346 A196531

Adjacent sequences: A365009 A365010 A365011 * A365013 A365014 A365015

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2023

Status

approved