%I A147564
%S A147564 1,1,1,1,4,1,1,11,9,1,1,16,24,12,1,1,21,46,42,15,1,1,26,75,100,65,18,1,
%T A147564 1,31,111,195,185,93,21,1,1,36,154,336,420,308,126,24,1,1,41,204,532,
%U A147564 826,798,476,164,27,1,1,46,261,792,1470,1764,1386,696,207,30,1,1,51,325
%N A147564 A set of Pascal triangle based polynomials: p(x,n)=If[n >= 0, -2 + 2*(1 
               + x)^n, 0] + (1 + x)^(1 + n) + If[n >1, 2*x*D[(1 + x)^n, {x, 1}], 
               0].
%C A147564 The row sums are:{1, 2, 6, 22, 54, 126, 286, 638, 1406, 3070, 6654, 14334,
               ...}
%F A147564 p(x,n)=If[n >= 0, -2 + 2*(1 + x)^n, 0] + (1 + x)^(1 + n) + If[n >1, 2*x*D[(1 
               + x)^n, {x, 1}], 0]; t(n,m)=coefficients(t(n,m)).
%e A147564 {1}, {1, 1}, {1, 4, 1}, {1, 11, 9, 1}, {1, 16, 24, 12, 1}, {1, 21, 46, 
               42, 15, 1}, {1, 26, 75, 100, 65, 18, 1}, {1, 31, 111, 195, 185, 93, 
               21, 1}, {1, 36, 154, 336, 420, 308, 126, 24, 1}, {1, 41, 204, 532, 
               826, 798, 476, 164, 27, 1}, {1, 46, 261, 792, 1470, 1764, 1386, 696, 
               207, 30, 1}, {1, 51, 325, 1125, 2430, 3486, 3402, 2250, 975, 255, 
               33, 1}
%t A147564 Clear[t, p, x, n]; p[x_, n_] = If[n >= 0, -2 + 2*(1 + x)^n,0] + (1 + 
               x)^(1 + n) + If[n > 1, 2*x*D[(1 + x)^n, {x, 1}], 0]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, 
               n]]], x], {n, -1, 10}]; Flatten[%]
%Y A147564 Sequence in context: A164366 A121692 A145271 this_sequence A090981 A087903 
               A112500
%Y A147564 Adjacent sequences: A147561 A147562 A147563 this_sequence A147565 A147566 
               A147567
%K A147564 nonn
%O A147564 -1,5
%A A147564 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 07 2008