A336961 Expansion of e.g.f. exp(x * (2 + x) * exp(x)).

1, 2, 10, 56, 384, 3022, 26626, 258624, 2734360, 31168682, 380196414, 4932536908, 67717987948, 979613124414, 14877703575130, 236469561581768, 3922587278751504, 67743812585483218, 1215417753459838198, 22609895367286957572, 435341977596130683316

Offset

0,2

Comments

Exponential transform of the oblong numbers (A002378).

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: exp(x * (2 + x) * exp(x)).

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

Mathematica

nmax = 20; CoefficientList[Series[Exp[x (2 + x) Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] k (k + 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Crossrefs

Cf. A000248, A002378, A033462, A209801, A216507, A279361, A336960.

Sequence in context: A097971 A191277 A290443 * A265954 A093303 A199163

Adjacent sequences: A336958 A336959 A336960 * A336962 A336963 A336964

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 09 2020

Status

approved