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%I A174004 #6 May 23 2012 10:29:29
%S A174004 1,1,1,2,1,1,5,2,1,1,12,6,2,1,1,30,16,7,2,1,1,76,46,20,8,2,1,1,195,
%T A174004 132,64,24,9,2,1,1,504,386,200,84,28,10,2,1,1,1309,1136,643,280,106,
%U A174004 32,11,2,1,1
%N A174004 A triangle based on:a(n,q)=a(n-1,q)+q*a(n-2,q);t(n,q)=If[n == 0, 1, Sum[Binomial[n, k]*a(k, q), {k, 1, n, 2}]]
%C A174004 Row sums are:
%C A174004 {1, 2, 4, 9, 22, 57, 154, 428, 1216, 3521,...}.
%F A174004 a(n,q)=a(n-1,q)+q*a(n-2,q);
%F A174004 t(n,q)=If[n == 0, 1, Sum[Binomial[n, k]*a(k, q), {k, 1, n, 2}]]
%e A174004 {1},
%e A174004 {1, 1},
%e A174004 {2, 1, 1},
%e A174004 {5, 2, 1, 1},
%e A174004 {12, 6, 2, 1, 1},
%e A174004 {30, 16, 7, 2, 1, 1},
%e A174004 {76, 46, 20, 8, 2, 1, 1},
%e A174004 {195, 132, 64, 24, 9, 2, 1, 1},
%e A174004 {504, 386, 200, 84, 28, 10, 2, 1, 1},
%e A174004 {1309, 1136, 643, 280, 106, 32, 11, 2, 1, 1}
%t A174004 Clear[t, n, q, a];
%t A174004 f[0, a_] := 0; f[1, a_] := 1;
%t A174004 f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];
%t A174004 t[n_, q_] = If[n == 0, 1, Sum[Binomial[n, k]*f[k, q], {k, 1, n, 2}]];
%t A174004 a = Table[Table[t[n, q], {n, 0, 10}], {q, 1, 11}];
%t A174004 Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
%t A174004 Flatten[%]
%K A174004 nonn,tabl,uned
%O A174004 0,4
%A A174004 _Roger L. Bagula_, Mar 05 2010

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