login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309084 a(n) = exp(3) * Sum_{k>=0} (-3)^k*k^n/k!. 3
1, -3, 6, -3, -21, 24, 195, -111, -3072, -4053, 57003, 277854, -697539, -12261567, -29861778, 371727465, 3511027599, 2028432480, -188521156857, -1470389129931, 1655487186864, 121873222577823, 915525253963023, -2095901567014530, -103715912230195863, -836215492271268459 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..571

FORMULA

G.f.: Sum_{j>=0} (-3)^j*x^j / Product_{k=1..j} (1 - k*x).

E.g.f.: exp(3*(1 - exp(x))).

a(n) = Sum_{k=0..n} (-3)^k * Stirling2(n,k).

MATHEMATICA

Table[Exp[3] Sum[(-3)^k k^n/k!, {k, 0, Infinity}], {n, 0, 25}]

Table[BellB[n, -3], {n, 0, 25}]

nmax = 25; CoefficientList[Series[Sum[(-3)^j x^j/Product[(1 - k x), {k, 1, j}] , {j, 0, nmax}], {x, 0, nmax}], x]

nmax = 25; CoefficientList[Series[Exp[3 (1 - Exp[x])], {x, 0, nmax}], x] Range[0, nmax]!

PROG

(MAGMA) [1] cat [(&+[((-3)^k*StirlingSecond(m, k)):k in [0..m]]):m in [1..25]]; // Marius A. Burtea, Jul 27 2019

CROSSREFS

Column k = 3 of A292861.

Cf. A000587, A027710, A213170, A309085, A317996.

Sequence in context: A205865 A085881 A265480 * A288092 A127574 A169842

Adjacent sequences:  A309081 A309082 A309083 * A309085 A309086 A309087

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jul 11 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 08:45 EDT 2019. Contains 328056 sequences. (Running on oeis4.)