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A291452
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Triangle read by rows, expansion of e.g.f. exp(x*(cos(z) + cosh(z) - 2)/2), nonzero coefficients of z.
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9
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1, 0, 1, 0, 1, 35, 0, 1, 495, 5775, 0, 1, 8255, 450450, 2627625, 0, 1, 130815, 35586525, 727476750, 2546168625, 0, 1, 2098175, 2941884000, 181262956875, 1932541986375, 4509264634875
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OFFSET
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0,6
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LINKS
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Table of n, a(n) for n=0..27.
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EXAMPLE
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Triangle starts:
[1]
[0, 1]
[0, 1, 35]
[0, 1, 495, 5775]
[0, 1, 8255, 450450, 2627625]
[0, 1, 130815, 35586525, 727476750, 2546168625]
[0, 1, 2098175, 2941884000, 181262956875, 1932541986375, 4509264634875]
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MAPLE
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CL := (f, x) -> PolynomialTools:-CoefficientList(f, x):
A291452_row := proc(n) exp(x*(cos(z)+cosh(z)-2)/2):
series(%, z, 88): CL((4*n)!*coeff(series(%, z, 4*(n+1)), z, 4*n), x) end:
for n from 0 to 7 do A291452_row(n) od;
# Alternative:
A291452row := proc(n) local P; 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:
CL(P(4, n), x); seq(%[k+1]/k!, k=0..n) end: # Peter Luschny, Sep 03 2018
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MATHEMATICA
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P[m_, n_] := P[m, n] = If[n == 0, 1, Sum[Binomial[m*n, m*k]*P[m, n - k]*x, {k, 1, n}]];
row[n_] := Module[{cl = CoefficientList[P[4, n], x]}, Table[cl[[k + 1]]/k!, {k, 0, n}]];
Table[row[n], {n, 0, 6}] // Flatten (* Jean-François Alcover, Jul 23 2019, after Peter Luschny *)
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CROSSREFS
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Cf. A048993 (m=1), A156289 (m=2), A291451 (m=3), this seq. (m=4).
Diagonal: A000012 (m=1), A001147 (m=2), A025035 (m=3), A025036 (m=4).
Row sums: A000110 (m=1), A005046 (m=2), A291973 (m=3), A291975 (m=4).
Alternating row sums: A000587 (m=1), A260884 (m=2), A291974 (m=3), A291976 (m=4).
Sequence in context: A250488 A236237 A067156 * A174593 A104785 A225313
Adjacent sequences: A291449 A291450 A291451 * A291453 A291454 A291455
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KEYWORD
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nonn,tabl
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AUTHOR
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Peter Luschny, Sep 07 2017
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STATUS
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approved
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