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 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 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

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