A371120 E.g.f. satisfies A(x) = 1 + x*A(x)^3*(exp(x*A(x)) - 1).

1, 0, 2, 3, 100, 545, 17946, 203497, 7194440, 132963777, 5172409630, 135827977241, 5868623306844, 200952952956769, 9665278822378466, 407661518051710665, 21789972653746494736, 1088515671895571005313, 64406426353877958253254, 3706048364249677363919929, 241519775363085819300229220

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n+2*k)! * Stirling2(n-k,k)/( (n-k)! * (n+k+1)! ).

Mathematica

Table[ n! * Sum[(n + 2 k)!*StirlingS2[n - k, k]/((n - k)!*(n + k + 1)!), {k, 0, Floor[n/2]}], {n, 0, 21}] (* Vincenzo Librandi, Mar 02 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (n+2*k)!*stirling(n-k, k, 2)/((n-k)!*(n+k+1)!));
(Magma) [Factorial(n)* &+[Factorial(n+2*k)*StirlingSecond(n-k, k) / (Factorial(n-k)* Factorial(n+k+1)): k in [0..Floor(n/2)] ] : n in [0..23] ]; // Vincenzo Librandi, Mar 02 2026

Crossrefs

Cf. A370988, A371115, A371119.

Cf. A371122.

Sequence in context: A323463 A212556 A171460 * A371270 A249409 A256114

Adjacent sequences: A371117 A371118 A371119 * A371121 A371122 A371123

Keyword

nonn

Author

Seiichi Manyama, Mar 11 2024

Extensions

More terms from Vincenzo Librandi, Mar 06 2026

Status

approved