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A298511 Central Lehmer-Comtet numbers of first kind: a(n) = A008296(2n,n). 2
1, 1, -1, -15, 49, 1365, -7645, -311311, 2475473, 132652377, -1367593305, -90881245455, 1151541572401, 91341008892445, -1373222414339685, -126594821384553375, 2202549127844351265, 231390624855674406705, -4573116447815658471025, -539278542630309415030735 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..386

FORMULA

a(n) = (2*n)!/n! * [x^(2*n)] ((1+x)*log(1+x))^n.

a(n) = Sum_{j=0..n} binomial(n+j,n) * n^j * Stirling1(2*n,n+j).

MAPLE

b:= proc(n, k) option remember; `if`(n=k, 1, `if`(k=0, 0,

      (n-1)*b(n-2, k-1)+b(n-1, k-1)+(k-n+1)*b(n-1, k)))

    end:

a:= n-> b(2*n, n):

seq(a(n), n=0..25);

CROSSREFS

Cf. A008275, A008296, A048994.

Sequence in context: A241577 A199899 A020257 * A103777 A134742 A318084

Adjacent sequences:  A298508 A298509 A298510 * A298512 A298513 A298514

KEYWORD

sign

AUTHOR

Alois P. Heinz, Jan 20 2018

STATUS

approved

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Last modified January 19 18:31 EST 2020. Contains 331052 sequences. (Running on oeis4.)