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 A219207 Triangle, read by rows, where T(n,k) = binomial(n,k)^(k+1) for n>=0, k=0..n. 4
 1, 1, 1, 1, 4, 1, 1, 9, 27, 1, 1, 16, 216, 256, 1, 1, 25, 1000, 10000, 3125, 1, 1, 36, 3375, 160000, 759375, 46656, 1, 1, 49, 9261, 1500625, 52521875, 85766121, 823543, 1, 1, 64, 21952, 9834496, 1680700000, 30840979456, 13492928512, 16777216, 1, 1, 81, 46656 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Maximal term in row n is asymptotically in position k = r*n, where r = A220359 = 0.70350607643... is a root of the equation (1-r)^(2*r-1) = r^(2*r). - Vaclav Kotesovec, Nov 15 2012 The matrix inverse starts 1; -1,1; 3,-4,1; -73,99,-27,1; 18055,-24496,6696,-256,1; -55694851,75563975,-20656000,790000,-3125,1; - R. J. Mathar, Mar 22 2013 LINKS Paul D. Hanna, Rows n = 0..45, flattened. FORMULA Row sums equal A184731. EXAMPLE Triangle of coefficients C(n,k)^(k+1) begins: 1; 1, 1; 1, 4, 1; 1, 9, 27, 1; 1, 16, 216, 256, 1; 1, 25, 1000, 10000, 3125, 1; 1, 36, 3375, 160000, 759375, 46656, 1; 1, 49, 9261, 1500625, 52521875, 85766121, 823543, 1; 1, 64, 21952, 9834496, 1680700000, 30840979456, 13492928512, 16777216, 1; ... MATHEMATICA Table[Binomial[n, k]^(k+1), {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Aug 15 2016 *) PROG (PARI) {T(n, k)=binomial(n, k)^(k+1)} for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print("")) CROSSREFS Cf. A184731, A219206, A184730. Sequence in context: A299427 A126062 A243608 * A157108 A056647 A056057 Adjacent sequences:  A219204 A219205 A219206 * A219208 A219209 A219210 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Nov 14 2012 STATUS approved

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Last modified June 16 13:44 EDT 2021. Contains 345057 sequences. (Running on oeis4.)