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A094418 Generalized ordered Bell numbers Bo(5,n). 23
1, 5, 55, 905, 19855, 544505, 17919055, 687978905, 30187495855, 1490155456505, 81732269223055, 4931150091426905, 324557348772511855, 23141780973332248505, 1776997406800302687055, 146197529083891406394905 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Fifth row of array A094416, which has more information.
LINKS
Paul Barry, Three Études on a sequence transformation pipeline, arXiv:1803.06408 [math.CO], 2018.
FORMULA
E.g.f.: 1/(6 - 5*exp(x)).
a(n) = Sum_{k=0..n} A131689(n,k)*5^k. - Philippe Deléham, Nov 03 2008
a(n) ~ n! / (6*(log(6/5))^(n+1)). - Vaclav Kotesovec, Mar 14 2014
a(0) = 1; a(n) = 5 * Sum_{k=1..n} binomial(n,k) * a(n-k). - Ilya Gutkovskiy, Jan 17 2020
a(0) = 1; a(n) = 5*a(n-1) - 6*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Nov 16 2023
MATHEMATICA
t = 30; Range[0, t]! CoefficientList[Series[1/(6 - 5 Exp[x]), {x, 0, t}], x] (* Vincenzo Librandi, Mar 16 2014 *)
PROG
(Magma)
A094416:= func< n, k | (&+[Factorial(j)*n^j*StirlingSecond(k, j): j in [0..k]]) >;
A094418:= func< k | A094416(5, k) >;
[A094418(n): n in [0..30]]; // G. C. Greubel, Jan 12 2024
(SageMath)
def A094416(n, k): return sum(factorial(j)*n^j*stirling_number2(k, j) for j in range(k+1)) # array
def A094418(k): return A094416(5, k)
[A094418(n) for n in range(31)] # G. C. Greubel, Jan 12 2024
(PARI) my(N=25, x='x+O('x^N)); Vec(serlaplace(1/(6 - 5*exp(x)))) \\ Joerg Arndt, Jan 15 2024
CROSSREFS
Sequence in context: A294051 A145662 A362653 * A365588 A367164 A008543
KEYWORD
nonn
AUTHOR
Ralf Stephan, May 02 2004
STATUS
approved

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Last modified June 15 08:58 EDT 2024. Contains 373402 sequences. (Running on oeis4.)