A171506 Coefficients of expansion polynomials related to fish weight allometric equation: p(x,t)=-Exp[t*x]*(1 - Exp[t/3])^3

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

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