A137433 - OEIS

%I #2 Mar 30 2012 17:34:26

%S 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 205,15,1,0,10800,19824,11494,2835,385,21,1,0,105840,216012,149212,

%U 45409,7000,658,28,1,0,1249920,2692080,2055500,740124,140889,15120,1050,36,1

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

%C Row sums:

%C {1, 1, 2, 12, 72, 480, 4320, 45360, 524160, 6894720, 101606400}

%C Row_sum(n)/n!=A000930(n)

%D Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150

%F 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 {1},

%e {0, 1},

%e {0, 1, 1},

%e {0, 8, 3, 1},

%e {0, 30, 35, 6, 1},

%e {0, 144, 230, 95, 10, 1},

%e {0, 1200, 1954, 945, 205, 15, 1},

%e {0, 10800, 19824, 11494, 2835, 385, 21, 1},

%e {0, 105840, 216012, 149212, 45409, 7000, 658, 28, 1},

%e {0, 1249920, 2692080, 2055500, 740124, 140889, 15120, 1050, 36, 1},

%e {0, 16692480, 37802736, 31266540, 12628160, 2814525, 370713, 29610, 1590, 45, 1}

%t 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 Cf. A000045, A000930.

%K nonn,tabl,uned

%O 1,8

%A _Roger L. Bagula_, Apr 17 2008