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A174672 Sequence A154693 adjusted to leading one:t(n,m)=A154693(n,m)-A154693(n,0)+1.

%I A174672 #4 Jun 02 2025 02:44:56
%S A174672 1,1,1,1,12,1,1,58,58,1,1,244,512,244,1,1,994,3592,3592,994,1,1,4016,
%T A174672 23756,38592,23756,4016,1,1,16174,154420,374728,374728,154420,16174,1,
%U A174672 1,65004,993088,3529104,4997824,3529104,993088,65004,1,1,260842,6314368
%N A174672 Sequence A154693 adjusted to leading one:t(n,m)=A154693(n,m)-A154693(n,0)+1.
%C A174672 Row sums are:
%C A174672 1, 2, 14, 118, 1002, 9174, 94138, 1090646, 14172218, 204490006, 3245253882,...
%F A174672 t(n,m)=A154693(n,m)-A154693(n,0)+1
%e A174672 {1},
%e A174672 {1, 1},
%e A174672 {1, 12, 1},
%e A174672 {1, 58, 58, 1},
%e A174672 {1, 244, 512, 244, 1},
%e A174672 {1, 994, 3592, 3592, 994, 1},
%e A174672 {1, 4016, 23756, 38592, 23756, 4016, 1},
%e A174672 {1, 16174, 154420, 374728, 374728, 154420, 16174, 1},
%e A174672 {1, 65004, 993088, 3529104, 4997824, 3529104, 993088, 65004, 1},
%e A174672 {1, 260842, 6314368, 32773312, 62896480, 62896480, 32773312, 6314368, 260842, 1},
%e A174672 {1, 1045480, 39684596, 299673344, 779048096, 1006350848, 779048096, 299673344, 39684596, 1045480, 1}
%t A174672 Clear[t, p, q, n, m];
%t A174672 p = 2; q = 1;
%t A174672 t[n_, m_] = (p^(n - m)*q^m + p^m*q^( n - m))*Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}];
%t A174672 Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
%t A174672 Flatten[%]
%Y A174672 A154690, A154692, A154693
%K A174672 nonn,tabl,uned
%O A174672 0,5
%A A174672 _Roger L. Bagula_, Mar 26 2010