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A263575 Stirling transform of Lucas numbers (A000032). 4
2, 1, 4, 14, 53, 227, 1092, 5791, 33350, 206511, 1365563, 9590847, 71216713, 556861216, 4569168866, 39222394456, 351304769679, 3275433717440, 31723522878974, 318571978752719, 3311400814816987, 35573458376435132, 394404160256111139, 4507130777468928696 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..23.

Eric Weisstein's MathWorld, Lucas Number.

Eric Weisstein's MathWorld, Stirling Transform.

Eric Weisstein's MathWorld, Bell Polynomial.

FORMULA

a(n) = Sum_{k=0..n} A000032(k)*stirling2(n,k).

Let phi = (1+sqrt(5))/2.

a(n) = B_n(phi)+B_n(1-phi), where B_n(x) is n-th Bell polynomial.

2*B_n(phi) = a(n) + A263576*sqrt(5).

E.g.f.: exp((exp(x)-1)*phi)+exp((exp(x)-1)*(1-phi)).

Sum_{k=0..n} a(k)*stirling1(n,k) = A000032(n).

G.f.: Sum_{j>=0} Lucas(j)*x^j / Product_{k=1..j} (1 - k*x). - Ilya Gutkovskiy, Apr 06 2019

MATHEMATICA

Table[Sum[LucasL[k] StirlingS2[n, k], {k, 0, n}], {n, 0, 23}]

Table[Simplify[BellB[n, GoldenRatio] + BellB[n, 1 - GoldenRatio]], {n, 0, 23}]

CROSSREFS

Cf. A000032, A213593, A005248, A061084, A263576.

Sequence in context: A006173 A102055 A232376 * A162977 A032174 A212267

Adjacent sequences:  A263572 A263573 A263574 * A263576 A263577 A263578

KEYWORD

nonn

AUTHOR

Vladimir Reshetnikov, Oct 21 2015

STATUS

approved

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)