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A337042 a(n) = exp(-1/6) * Sum_{k>=0} (6*k - 1)^n / (6^k * k!). 5
1, 0, 6, 36, 324, 3456, 43416, 618192, 9778320, 169827840, 3210376032, 65540155968, 1435094563392, 33510354739200, 830486180748672, 21756166766173440, 600339119317643520, 17394883290643709952, 527782830161632077312, 16727350847049194775552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

G.f. A(x) satisfies: A(x) = (1 - 6*x + x*A(x/(1 - 6*x))) / (1 - 5*x - 6*x^2).

G.f.: (1/(1 + x)) * Sum_{k>=0} (x/(1 + x))^k / Product_{j=1..k} (1 - 6*j*x/(1 + x)).

E.g.f.: exp((exp(6*x) - 1) / 6 - x).

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

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A005012(k).

MATHEMATICA

nmax = 19; CoefficientList[Series[Exp[(Exp[6 x] - 1)/6 - x], {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k] 6^k a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 19}]

Table[Sum[(-1)^(n - k) Binomial[n, k] 6^k BellB[k, 1/6], {k, 0, n}], {n, 0, 19}]

CROSSREFS

Cf. A000296, A003578, A005012, A337038, A337039, A337040, A337041, A337043.

Sequence in context: A138418 A064239 A047898 * A098559 A129584 A052559

Adjacent sequences:  A337039 A337040 A337041 * A337043 A337044 A337045

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 12 2020

STATUS

approved

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Last modified July 24 08:43 EDT 2021. Contains 346273 sequences. (Running on oeis4.)