A355114 Expansion of e.g.f. 6 / (7 - 6*x - exp(6*x)).

1, 2, 14, 156, 2256, 40416, 869040, 21817440, 626063616, 20210176512, 724888631808, 28599923045376, 1230970377166848, 57397448756994048, 2882187551571941376, 155065468075097960448, 8898907099302329647104, 542609247778976191610880, 35031706496702707368591360

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} binomial(n,k) * 6^(k-1) * a(n-k).

a(n) ~ n! / ((1 + LambertW(exp(7))) * ((7 - LambertW(exp(7)))/6)^(n+1)). - Vaclav Kotesovec, Jun 19 2022

Mathematica

nmax = 18; CoefficientList[Series[6/(7 - 6 x - Exp[6 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 6^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

Crossrefs

Cf. A003578, A006155, A094419, A355110, A355111, A355112, A355113.

Sequence in context: A060193 A222200 A175564 * A332693 A196791 A349312

Adjacent sequences: A355111 A355112 A355113 * A355115 A355116 A355117

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 19 2022

Status

approved