login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A171506 Coefficients of expansion polynomials related to fish weight allometric equation: p(x,t)=-Exp[t*x]*(1 - Exp[t/3])^3 0
6, 36, 72, 150, 540, 540, 540, 2700, 4860, 3240, 1806, 11340, 28350, 34020, 17010, 5796, 43344, 136080, 226800, 204120, 81648, 18150, 156492, 585144, 1224720, 1530900, 1102248, 367416, 55980, 544500, 2347380, 5851440, 9185400, 9185400 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

The fish weight population equation comes from a systems theory approach to population problems.

Row sums are;

{6, 108, 1230, 11340, 92526, 697788, 4985070, 34255980, 228718446, 1494160668,

9598316910,...}.

REFERENCES

Ludwig von Bertalanffy, General Systems Theory, George Braziller publisher, New York, 1968, page 174-5

LINKS

Table of n, a(n) for n=3..36.

FORMULA

p(x,t)=-Exp[t*x]*(1 - Exp[t/3])^3

EXAMPLE

{6},

{36, 72},

{150, 540, 540},

{540, 2700, 4860, 3240},

{1806, 11340, 28350, 34020, 17010},

{5796, 43344, 136080, 226800, 204120, 81648},

{18150, 156492, 585144, 1224720, 1530900, 1102248, 367416},

{55980, 544500, 2347380, 5851440, 9185400, 9185400, 5511240, 1574640},

{171006, 1847340, 8984250, 25821180, 48274380, 60623640, 50519700, 25981560, 6495390},

{519156, 6156216, 33252120, 107811000, 232390620, 347575536, 363741840, 259815600, 116917020, 25981560},

{1569750, 20247084, 120046212, 432277560, 1051157250, 1812646836, 2259240984, 2026561680, 1266601050, 506640420, 101328084}

MATHEMATICA

p[t_] = -Exp[t*x]*(1 - Exp[t/3])^3

a = Table[ CoefficientList[FullSimplify[ExpandAll[3^n* n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 3, 13}]

Flatten[a]

CROSSREFS

Cf. A096084, A096086, A117655

Sequence in context: A119845 A208064 A207929 * A207683 A207509 A207846

Adjacent sequences:  A171503 A171504 A171505 * A171507 A171508 A171509

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 10 2009

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 November 30 18:54 EST 2021. Contains 349424 sequences. (Running on oeis4.)