A390373 Expansion of e.g.f. (1/2) * (exp(1/(1 - x)^2 - 1) + 1).

1, 1, 5, 34, 290, 2956, 34892, 466600, 6956168, 114195280, 2044297232, 39593226784, 824198178080, 18339085306816, 434119727399360, 10888176248977024, 288314558327931008, 8034883301194942720, 235007894463566519552, 7196007297036317893120, 230161142318670903607808, 7673996503266988619262976

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * Bell(k) * 2^(k-1) for n > 0.

a(n) = A136658(n) / 2 for n > 0.

Mathematica

nmax = 21; CoefficientList[Series[(1/2) (Exp[1/(1 - x)^2 - 1] + 1), {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[Sum[(-1)^(n - k) StirlingS1[n, k] BellB[k] 2^(k - 1), {k, 1, n}], {n, 1, 21}]]

Crossrefs

Cf. A000262, A000902, A055882, A136658, A346417, A390374.

Sequence in context: A208677 A380619 A379203 * A259906 A379991 A355258

Adjacent sequences: A390370 A390371 A390372 * A390374 A390375 A390376

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 03 2025

Status

approved