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 A174673 Triangle read by rows: T(n,m)=A154694(n,m)-A154694(n,0)+1. 1
 1, 1, 1, 1, 36, 1, 1, 296, 296, 1, 1, 1932, 4656, 1932, 1, 1, 11696, 54086, 54086, 11696, 1, 1, 69048, 556596, 1042920, 556596, 69048, 1, 1, 405236, 5406866, 16866206, 16866206, 5406866, 405236, 1, 1, 2381700, 51004320, 247754256, 404837664 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Reduces the values in the triangle A154694 such that each row starts with 1. Row sums are: 1, 2, 38, 594, 8522, 131566, 2294210, 45356618, 1007118218, 24839902470, 673894929842,... LINKS Table of n, a(n) for n=0..40. FORMULA t(n,m)=A154694(n,m)-A154694(n,0)+1 EXAMPLE {1}, {1, 1}, {1, 36, 1}, {1, 296, 296, 1}, {1, 1932, 4656, 1932, 1}, {1, 11696, 54086, 54086, 11696, 1}, {1, 69048, 556596, 1042920, 556596, 69048, 1}, {1, 405236, 5406866, 16866206, 16866206, 5406866, 405236, 1}, {1, 2381700, 51004320, 247754256, 404837664, 247754256, 51004320, 2381700, 1}, {1, 14050376, 473595806, 3441231326, 8491073726, 8491073726, 3441231326, 473595806, 14050376, 1}, {1, 83216400, 4357421004, 46167420504, 164067684600, 244543444824, 164067684600, 46167420504, 4357421004, 83216400, 1} MAPLE A174673 := proc(n, m) A154694(n, m)-A154694(n, 0)+1 ; end proc: seq(seq( A174673(n, m), m=0..n), n=0..10) ; # R. J. Mathar, Mar 11 2024 MATHEMATICA Clear[t, p, q, n, m]; p = 2; q = 3; 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}]; Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS A154690, A154692, A154693, A154964 Sequence in context: A309379 A022071 A181635 * A203277 A156645 A330084 Adjacent sequences: A174670 A174671 A174672 * A174674 A174675 A174676 KEYWORD nonn,tabl,less AUTHOR Roger L. Bagula, Mar 26 2010 STATUS approved

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Last modified July 14 22:52 EDT 2024. Contains 374323 sequences. (Running on oeis4.)