The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 11 16:12 EDT 2021. Contains 342886 sequences. (Running on oeis4.)