A365016 E.g.f. satisfies A(x) = exp( x*A(x)^3/(1 - x * A(x)^2) ).

1, 1, 9, 160, 4345, 159796, 7434199, 418864426, 27732988609, 2110729489048, 181587635465671, 17426825999144926, 1845855944285411425, 213900244312057975348, 26919356609721984494311, 3656322063766897691641666, 533110345129065969043548289

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..325

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, #}] &, 17, 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. A361066, A361094, A365015.

Cf. A212722, A361093, A361143, A365012.

Sequence in context: A360777 A309472 A060348 * A367163 A363479 A217392

Adjacent sequences: A365013 A365014 A365015 * A365017 A365018 A365019

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2023

Status

approved