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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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..27.

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-Fran├žois 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: A250488 A236237 A067156 * A174593 A104785 A225313

Adjacent sequences:  A291449 A291450 A291451 * A291453 A291454 A291455

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Sep 07 2017

STATUS

approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)