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A137433 Coefficients of A000930 expansion similar to that given for Fibonacci numbers in Roman's Umbral Calculus.

%I A137433 #2 Mar 30 2012 17:34:26
%S A137433 1,0,1,0,1,1,0,8,3,1,0,30,35,6,1,0,144,230,95,10,1,0,1200,1954,945,
%T A137433 205,15,1,0,10800,19824,11494,2835,385,21,1,0,105840,216012,149212,
%U A137433 45409,7000,658,28,1,0,1249920,2692080,2055500,740124,140889,15120,1050,36,1
%N A137433 Coefficients of A000930 expansion similar to that given for Fibonacci numbers in Roman's Umbral Calculus.
%C A137433 Row sums:
%C A137433 {1, 1, 2, 12, 72, 480, 4320, 45360, 524160, 6894720, 101606400}
%C A137433 Row_sum(n)/n!=A000930(n)
%D A137433 Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150
%F A137433 Coefficients expansion of p(x,n) in f(x,t)=1/(1-t-t^3)^x=Sum[p(x,n)*t^n/n!m{n,1,Infinity}]
%e A137433 {1},
%e A137433 {0, 1},
%e A137433 {0, 1, 1},
%e A137433 {0, 8, 3, 1},
%e A137433 {0, 30, 35, 6, 1},
%e A137433 {0, 144, 230, 95, 10, 1},
%e A137433 {0, 1200, 1954, 945, 205, 15, 1},
%e A137433 {0, 10800, 19824, 11494, 2835, 385, 21, 1},
%e A137433 {0, 105840, 216012, 149212, 45409, 7000, 658, 28, 1},
%e A137433 {0, 1249920, 2692080, 2055500, 740124, 140889, 15120, 1050, 36, 1},
%e A137433 {0, 16692480, 37802736, 31266540, 12628160, 2814525, 370713, 29610, 1590, 45, 1}
%t A137433 Clear[p, g]; p[t_] = 1/(1 - t - t^3)^x; Table[ ExpandAll[n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
%Y A137433 Cf. A000045, A000930.
%K A137433 nonn,tabl,uned
%O A137433 1,8
%A A137433 _Roger L. Bagula_, Apr 17 2008