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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137524 Triangular sequence from coefficients of the umbral calculus expansion of a Golden -Mean Bernoulli function(A001898): p(x,t)=t*phi^(x*t)/(phi^t - 1), where the golden ratio replaces "e". 0
2, -3, 6, 4, -24, 24, 0, 60, -180, 120, -24, 0, 720, -1440, 720, 0, -840, 0, 8400, -12600, 5040, 960, 0, -20160, 0, 100800, -120960, 40320, 0, 60480, 0, -423360, 0, 1270080, -1270080, 362880, -120960, 0, 2419200, 0, -8467200, 0, 16934400, -14515200, 3628800, 0, -11975040, 0, 79833600, 0, -167650560, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are: {2, 3, 4, 0, -24, 0, 960, 0, -120960, 0, 36288000}

These are the same as the Bernoulli numbers with the factor log(phi)^n: p[t_] = t*Exp[x*t]/(Exp[t] - 1);

a = Table[ CoefficientList[(n + 2)!*n!*SeriesCoefficient[Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}].

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

{2},

{-3, 6},

{4, -24, 24},

{0, 60, -180, 120},

{-24, 0, 720, -1440, 720},

{0, -840, 0, 8400, -12600, 5040},

{960, 0, -20160, 0, 100800, -120960, 40320},

{0, 60480, 0, -423360, 0, 1270080, -1270080, 362880},

{-120960, 0, 2419200, 0, -8467200, 0, 16934400, -14515200, 3628800},

{0, -11975040, 0, 79833600, 0, -167650560, 0, 239500800, -179625600, 39916800}, {36288000, 0, -718502400, 0, 2395008000, 0, -3353011200, 0, 3592512000, -2395008000, 479001600}

MATHEMATICA

p[t_]=t*GoldenRatio^(x*t)/(GoldenRatio^t-1); Table[ ExpandAll[((n+2)!*n!/Log[GoldenRatio]^(n-1))*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a=Table[ CoefficientList[((n+2)!*n!/Log[GoldenRatio]^(n-1))*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[((n+2)!*n!/Log[GoldenRatio]^(n-1))*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x]], {n, 0, 10}];

CROSSREFS

Cf. A001898.

Sequence in context: A214352 A248090 A229774 * A282507 A156055 A096357

Adjacent sequences:  A137521 A137522 A137523 * A137525 A137526 A137527

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula, Apr 27 2008

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 18 03:43 EST 2018. Contains 299298 sequences. (Running on oeis4.)