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A079563 a(n) = a(n,m) = sum(k=0,n,binomial(m*k,k)*binomial(m*(n-k),n-k)) for m=7. 0
1, 14, 231, 3934, 67851, 1177974, 20531770, 358788696, 6281076123, 110103674128, 1931983053056, 33926800240578, 596145343139514, 10480467311987778, 184327560283768776, 3243034966775972144, 57074433199551436347 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

More generally : a(n,m) = sum(k=0,n,binomial(m*k,k)*binomial(m*(n-k),n-k)) is asymptotic to 1/2*m/(m-1)*(m^m/(m-1)^(m-1))^n. See A000302, A006256, A078995 for cases m=2,3 and 4.

LINKS

Table of n, a(n) for n=0..16.

D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344.

Rui Duarte and António Guedes de Oliveira, Short note on the convolution of binomial coefficients, arXiv:1302.2100 [math.CO], 2013.

FORMULA

a(n) = (7/12)*(823543/46656)^n*(1+c/sqrt(n)+o(n^-1/2)) where c=0.41...

a(n) = sum(k=0,n,binomial(7*k+l,k)*binomial(7*(n-k)-l,n-k)) for every real number l. - Rui Duarte and António Guedes de Oliveira, Feb 16 2013

a(n) = sum(k=0,n,6^(n-k)*binomial(7n+1,k)). - Rui Duarte and António Guedes de Oliveira, Feb 17 2013

a(n) = sum(k=0,n,7^(n-k)*binomial(6n+k,k)). - Rui Duarte and António Guedes de Oliveira, Feb 17 2013

CROSSREFS

Sequence in context: A099272 A273625 A120048 * A230346 A280559 A305862

Adjacent sequences:  A079560 A079561 A079562 * A079564 A079565 A079566

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jan 26 2003

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)