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A282179 E.g.f.: exp(exp(x) - 1)*(exp(3*x) - 2*exp(x) + 1). 1
0, 1, 9, 52, 283, 1561, 8930, 53411, 334785, 2199034, 15119621, 108644581, 814474176, 6358910949, 51615342685, 434865155292, 3796991928727, 34308796490005, 320379418256794, 3087939032182127, 30683582797977749, 313977721545709002, 3305220440084030809, 35759627532783842561 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Stirling transform of the cubes (A000578).
Exponential convolution of the sequences A000110 and A058481 (with a(0) = 0).
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Eric Weisstein's MathWorld, Stirling Transform
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k)*A000578(k).
a(n) = A000110(n) + A005494(n) - A186021(n+1).
EXAMPLE
E.g.f.: A(x) = x/1! + 9*x^2/2! + 52*x^3/3! + 283*x^4/4! + 1561*x^5/5! + 8930*x^6/6! + ...
MAPLE
b:= proc(n, m) option remember; `if`(n=0,
m^3, m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..27); # Alois P. Heinz, Jul 15 2022
MATHEMATICA
Range[0, 23]! CoefficientList[Series[Exp[Exp[x] - 1] (Exp[3 x] - 2 Exp[x] + 1), {x, 0, 23}], x]
Table[Sum[StirlingS2[n, k] k^3, {k, 0, n}], {n, 0, 23}]
Table[Sum[Binomial[n, k] BellB[n-k] (3^k - 2), {k, 1, n}], {n, 0, 23}]
Table[BellB[n+3] - 3*BellB[n+2] + BellB[n], {n, 0, 23}] (* Vaclav Kotesovec, Aug 06 2021 *)
CROSSREFS
Sequence in context: A163941 A289418 A292488 * A278000 A159598 A279358
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 08 2017
STATUS
approved

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Last modified June 21 14:19 EDT 2024. Contains 373547 sequences. (Running on oeis4.)