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 A278074 Triangle read by rows, coefficients of the polynomials P(m, n) = Sum_{k=1..n} binomial(m*n, m*k)* P(m, n-k)*z with P(m, 0) = 1 and m = 4. 12
 1, 0, 1, 0, 1, 70, 0, 1, 990, 34650, 0, 1, 16510, 2702700, 63063000, 0, 1, 261630, 213519150, 17459442000, 305540235000, 0, 1, 4196350, 17651304000, 4350310965000, 231905038365000, 3246670537110000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Robert Israel, Table of n, a(n) for n = 0..8510 FORMULA E.g.f.: 1/(1-t*((cosh(x)+cos(x))/2-1)), nonzero terms. EXAMPLE Triangle starts: [1] [0, 1] [0, 1, 70] [0, 1, 990, 34650] [0, 1, 16510, 2702700, 63063000] [0, 1, 261630, 213519150, 17459442000, 305540235000] MAPLE P := proc(m, n) option remember; if n = 0 then 1 else add(binomial(m*n, m*k)* P(m, n-k)*x, k=1..n) fi end: for n from 0 to 6 do PolynomialTools:-CoefficientList(P(4, n), x) od; # Alternatively: A278074_row := proc(n) 1/(1-t*((cosh(x)+cos(x))/2-1)); expand(series(%, x, 4*n+1)); (4*n)!*coeff(%, x, 4*n); PolynomialTools:-CoefficientList(%, t) end: for n from 0 to 5 do A278074_row(n) od; MATHEMATICA With[{m = 4}, Table[Expand[j!*SeriesCoefficient[1/(1 - t*(MittagLefflerE[m, x^m] - 1)), {x, 0, j}]], {j, 0, 24, m}]]; Function[arg, CoefficientList[arg, t]] /@ % // Flatten PROG (Sage) # uses [P from A278073] def A278074_row(n): return list(P(4, n)) for n in (0..6): print(A278074_row(n)) # Peter Luschny, Mar 24 2020 CROSSREFS Cf. A014608 (diagonal), A243665 (row sums), A211212 (alternating row sums), A281480 (central coefficients). Cf. A097805 (m=0), A131689 (m=1), A241171 (m=2), A278073 (m=3). Cf. A327024 (refinement). Sequence in context: A116238 A136114 A365913 * A075405 A365914 A177808 Adjacent sequences: A278071 A278072 A278073 * A278075 A278076 A278077 KEYWORD nonn,tabl AUTHOR Peter Luschny, Jan 22 2017 STATUS approved

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Last modified August 2 21:08 EDT 2024. Contains 374875 sequences. (Running on oeis4.)