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%I #2 Mar 30 2012 17:34:36
%S 6,36,72,150,540,540,540,2700,4860,3240,1806,11340,28350,34020,17010,
%T 5796,43344,136080,226800,204120,81648,18150,156492,585144,1224720,
%U 1530900,1102248,367416,55980,544500,2347380,5851440,9185400,9185400
%N Coefficients of expansion polynomials related to fish weight allometric equation: p(x,t)=-Exp[t*x]*(1 - Exp[t/3])^3
%C The fish weight population equation comes from a systems theory approach to population problems.
%C Row sums are;
%C {6, 108, 1230, 11340, 92526, 697788, 4985070, 34255980, 228718446, 1494160668,
%C 9598316910,...}.
%D Ludwig von Bertalanffy, General Systems Theory, George Braziller publisher, New York, 1968, page 174-5
%F p(x,t)=-Exp[t*x]*(1 - Exp[t/3])^3
%e {6},
%e {36, 72},
%e {150, 540, 540},
%e {540, 2700, 4860, 3240},
%e {1806, 11340, 28350, 34020, 17010},
%e {5796, 43344, 136080, 226800, 204120, 81648},
%e {18150, 156492, 585144, 1224720, 1530900, 1102248, 367416},
%e {55980, 544500, 2347380, 5851440, 9185400, 9185400, 5511240, 1574640},
%e {171006, 1847340, 8984250, 25821180, 48274380, 60623640, 50519700, 25981560, 6495390},
%e {519156, 6156216, 33252120, 107811000, 232390620, 347575536, 363741840, 259815600, 116917020, 25981560},
%e {1569750, 20247084, 120046212, 432277560, 1051157250, 1812646836, 2259240984, 2026561680, 1266601050, 506640420, 101328084}
%t p[t_] = -Exp[t*x]*(1 - Exp[t/3])^3
%t a = Table[ CoefficientList[FullSimplify[ExpandAll[3^n* n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 3, 13}]
%t Flatten[a]
%Y Cf. A096084, A096086, A117655
%K nonn,uned,tabl
%O 3,1
%A _Roger L. Bagula_, Dec 10 2009
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