A390889 a(n) = Sum_{k=0..n} 2^k * 5^(n-k) * Stirling2(n,k).

1, 2, 14, 118, 1206, 14582, 202214, 3142598, 53897526, 1008806742, 20424419974, 444041431398, 10303933241686, 253914869006582, 6616159350544294, 181609905062298118, 5234530286774772086, 157971376628934193302, 4978974300820205042374, 163522731843049569902758

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..441

Formula

G.f.: Sum_{k>=0} (2*x)^k / Product_{j=1..k} (1 - 5*j*x).

E.g.f.: exp( 2*(exp(5*x)-1)/5 ).

a(n) = exp(-2/5) * Sum_{k>=0} 2^k * 5^(n-k) * k^n/k!.

a(0) = 1; a(n) = 2 * Sum_{k=1..n} 5^(k-1) * binomial(n-1,k-1) * a(n-k).

Mathematica

Join[{1}, Table[Sum[2^k*5^(n-k)*StirlingS2[n, k], {k, 0, n}], {n, 25}]] (* Vincenzo Librandi, Jan 04 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, 2^k*5^(n-k)*stirling(n, k, 2));
(Magma) [1] cat [&+[2^k*5^(n-k)*StirlingSecond(n, k): k in [0..n]]: n in [1..25]]; // Vincenzo Librandi, Jan 04 2026

Crossrefs

Cf. A001861, A055882, A390888.

Cf. A047055.

Sequence in context: A208393 A370671 A361962 * A192457 A351856 A394763

Adjacent sequences: A390886 A390887 A390888 * A390890 A390891 A390892

Keyword

nonn

Author

Seiichi Manyama, Nov 22 2025

Status

approved