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A166357 Exponential Riordan array [1+x*arctanh(x), x]. 3
1, 0, 1, 2, 0, 1, 0, 6, 0, 1, 8, 0, 12, 0, 1, 0, 40, 0, 20, 0, 1, 144, 0, 120, 0, 30, 0, 1, 0, 1008, 0, 280, 0, 42, 0, 1, 5760, 0, 4032, 0, 560, 0, 56, 0, 1, 0, 51840, 0, 12096, 0, 1008, 0, 72, 0, 1, 403200, 0, 259200, 0, 30240, 0, 1680, 0, 90, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are A166358. Diagonal sums are A166359.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1274 (rows 0..49)

FORMULA

Number triangle T(n,k) = [k<=n]*A166356((n-k)/2)*C(n,k)*(1+(-1)^(n-k))/2.

EXAMPLE

Triangle begins

       1;

       0,     1;

       2,     0,      1;

       0,     6,      0,     1;

       8,     0,     12,     0,     1;

       0,    40,      0,    20,     0,    1;

     144,     0,    120,     0,    30,    0,    1;

       0,  1008,      0,   280,     0,   42,    0,  1;

    5760,     0,   4032,     0,   560,    0,   56,  0,  1;

       0, 51840,      0, 12096,     0, 1008,    0, 72,  0, 1;

  403200,     0, 259200,     0, 30240,    0, 1680,  0, 90, 0, 1;

PROG

(PARI) T(n, k)={binomial(n, k)*(n-k)!*polcoef(1 + x*atanh(x + O(x^max(1, n-k))), n-k)} \\ Andrew Howroyd, Aug 17 2018

(PARI) T(n, k)=if(k>=n, n==k, binomial(n, k)*if((n-k)%2, 0, (n-k-1)! + (n-k-2)!)) \\ Andrew Howroyd, Aug 17 2018

CROSSREFS

Sequence in context: A166335 A109187 A265089 * A067147 A112227 A166378

Adjacent sequences:  A166354 A166355 A166356 * A166358 A166359 A166360

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 12 2009

STATUS

approved

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Last modified March 20 07:42 EDT 2019. Contains 321345 sequences. (Running on oeis4.)