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A082759
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a(n) = sum_{k=0..n} binomial(n,k) trinomial(n,k), where trinomial(n,k) = trinomial coefficients.
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5
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1, 2, 8, 35, 160, 752, 3599, 17446, 85376, 420884, 2087008, 10398016, 52010479, 261021854, 1313707256, 6628095035, 33512880640, 169768235840, 861450392708, 4377796514152, 22277498220160, 113502759811000, 578931209245760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Central coefficients of A115990. [Paul Barry, Feb 25 2011]
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FORMULA
| a(n)=sum(k=0, n, C(n+k, n-k)*C(n, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 20 2003
2*n*(2*n - 1)*(38*n - 53)*a(n) + ( - 760*n^3 + 1820*n^2 - 1252*n + 252)*a(n - 1) - 8*(n - 1)*(19*n^2 - 36*n + 9)*a(n - 2) - 3*(38*n - 15)*(n - 1)*(n - 2)*a(n - 3) = 0. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 15 2004
a(n)=sum{k=0..n, C(2n-k, k)*C(n, k)} - Paul Barry (pbarry(AT)wit.ie), Jan 20 2005
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PROG
| (PARI) a(n)=sum(k=0, n, binomial(n+k, n-k)*binomial(n, k))
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CROSSREFS
| Cf. A037011.
Sequence in context: A037723 A037618 A184786 * A137265 A129580 A007034
Adjacent sequences: A082756 A082757 A082758 * A082760 A082761 A082762
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KEYWORD
| easy,nonn
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AUTHOR
| Emanuele Munarini (munarini(AT)mate.polimi.it), May 21 2003
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