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A162171 Third column of A162170. 1
1, 3, 6, 20, 75, 336, 1708, 9792, 62325, 436480, 3334386, 27595776, 245951615, 2348666880, 23923317720, 258910994432, 2966901358185, 35886973648896, 456927138333790, 6108665873694720, 85555744482868275, 1252729007440396288, 19140289332506060676 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..23.

FORMULA

a(n) = Sum_{k=1..floor(n/2)} (-1)^(floor(n/2)+k) * binomial(n+1, 2*k) * a(2*k-1) for n > 1. - Mike Tryczak, Jun 18 2015

a(n) = n*(n+1)/2 * A000111(n-1) (conjectured). - Mike Tryczak, Jun 17 2015

PROG

(PARI) T(n, k) = if (k % 2, binomial(n-1, k-1) * (-1)^floor((n+k-1)/2), if (n==k, 1 , 0));

lista(nn) = {m = matrix(nn, nn, n, k, if (n>=k, T(n, k), 0)); m = m^(-1); for (n=3, nn, print1(m[n, 3], ", ")); } \\ Michel Marcus, Jun 17 2015

(PARI) lista(nn) = { a = [1]; for(n = 2, nn, a = concat(a, sum(k = 1, j = floor(n/2), (-1)^(j+k) * binomial(n+1, 2*k) * a[2*k-1]))); print(a) } \\ Mike Tryczak, Jun 18 2015

CROSSREFS

Cf. A162170, A000111.

Sequence in context: A288817 A168594 A123559 * A194992 A163881 A238474

Adjacent sequences:  A162168 A162169 A162170 * A162172 A162173 A162174

KEYWORD

nonn

AUTHOR

Mats Granvik, Jun 27 2009

EXTENSIONS

Sequence corrected and extended by Mike Tryczak, Jun 17 2015

STATUS

approved

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Last modified August 26 03:18 EDT 2019. Contains 326324 sequences. (Running on oeis4.)