A390887 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * Stirling2(n,k).

1, 3, 15, 93, 681, 5691, 53079, 544053, 6058545, 72652179, 931542207, 12697268205, 183092096409, 2781622021899, 44367455166279, 740692876276101, 12907778812456929, 234245590139848611, 4417503444286366191, 86405523372046968573, 1749924601146886483977

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Formula

G.f.: Sum_{k>=0} (3*x)^k / Product_{j=1..k} (1 - 2*j*x).

E.g.f.: exp( 3*(exp(2*x)-1)/2 ).

a(n) = exp(-3/2) * Sum_{k>=0} 3^k * 2^(n-k) * k^n/k!.

a(0) = 1; a(n) = 3 * Sum_{k=1..n} 2^(k-1) * binomial(n-1,k-1) * a(n-k).

Mathematica

Join[{1}, Table[Sum[3^k*2^(n-k)*StirlingS2[n, k], {k, 0, n}], {n, 25}]] (* Vincenzo Librandi, Jan 04 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, 3^k*2^(n-k)*stirling(n, k, 2));
(Magma) [1] cat [&+[3^k*2^(n-k)*StirlingSecond(n, k): k in [0..n]]: n in [1..25]]; // Vincenzo Librandi, Jan 04 2026

Crossrefs

Cf. A004211, A055882.

Sequence in context: A060066 A206177 A366638 * A272230 A308457 A241711

Adjacent sequences: A390884 A390885 A390886 * A390888 A390889 A390890

Keyword

nonn

Author

Seiichi Manyama, Nov 22 2025

Status

approved