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A291452
Triangle read by rows, expansion of e.g.f. exp(x*(cos(z) + cosh(z) - 2)/2), nonzero coefficients of z.
11
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
OFFSET
0,6
EXAMPLE
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]
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
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: A236237 A067156 A365894 * A343981 A174593 A104785
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 07 2017
STATUS
approved