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A012250 A012249(2n) divided by 2^(2n-1). 2
1, 3, 40, 1225, 67956, 5986134, 769550496, 136151219061, 31753157473180, 9445432588519642, 3491687484842443536, 1570713950508131878618, 845034544811095556274280, 535857105694970626486925100, 395590680969537758258609408640, 336386798400777928783348084420365 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

D. N. Verma, Towards Classifying Finite Point-Set Configurations, preprint, 1997.

LINKS

Table of n, a(n) for n=1..16.

M. Hering, B. Howard, The ring of evenly weighted points on the line, arXiv:1211.3941 [math.AG], 2012-2014, see p. 8.

B. Howard, J. Millson, A. Snowden, R. Vakil, The moduli space of n points on the line is cut out by simple quadrics when n is not six, p. 12.

Richard Stanley, Access to a preprint by D. N. Verma.

R. P Stanley and F. Zanello, Unimodality of partitions with distinct parts inside Ferrers shapes, see Theorem 4.6.

R. P Stanley and F. Zanello, Unimodality of partitions with distinct parts inside Ferrers shapes, arXiv:1305.6083 [math.CO], 2013, see Theorem 4.6 and Remark 4.7.

R. P Stanley and F. Zanello, Unimodality of partitions with distinct parts inside Ferrers shapes, European Journal of Combinatorics, Volume 49, October 2015, Pages 194-202.

FORMULA

a(n) = (1/2)*sum(j=0..n, (-1)^(j+1)*binomial(2*n+2,j)*(n-j+1)^(2*n-1)). - Richard Stanley, Mar 31 2013

MAPLE

A012250 := n -> 1/2*add((-1)^(j+1)*binomial(2*n+2, j)*(n-j+1)^(2*n-1)*(2*j-2*n-1), j=0..n); seq(A012250(i), i=1..9); # Peter Luschny, Mar 03 2013

MATHEMATICA

Table[Sum[(-1)^(j + 1)*Binomial[2*n + 2, j]*(n - j + 1)^(2*n - 1)/2, {j, 0, n}], {n, 15}] (* Wesley Ivan Hurt, Nov 11 2014 *)

CROSSREFS

Cf. A012249.

Sequence in context: A260754 A047799 A204515 * A094330 A110468 A327356

Adjacent sequences:  A012247 A012248 A012249 * A012251 A012252 A012253

KEYWORD

nonn

AUTHOR

D n Verma

EXTENSIONS

Edited and extended using Richard Stanley's formula. - N. J. A. Sloane, Jun 10 2013

STATUS

approved

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)