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A055835
T(2n+1,n), where T is the array in A055830.
3
1, 3, 12, 54, 255, 1239, 6132, 30744, 155628, 793650, 4071210, 20984340, 108590118, 563816526, 2935798680, 15324533448, 80164934919, 420151515255, 2205762626010, 11597513662350, 61060181223195, 321870918101535
OFFSET
0,2
LINKS
FORMULA
a(n) = 3*A055834(n) for n>=1. - Philippe Deléham, Jan 25 2014
a(n) = Sum_{k=0..n} Sum_{i=k..n} binomial(i,k)*binomial(i+1,n-i)*binomial(n,k). - Vladimir Kruchinin, Mar 01 2014
MAPLE
seq( `if`(n=0, 1, 3*add(binomial(n+k-1, n)*binomial(k, n-k), k=0..n)), n=0..30); # G. C. Greubel, Jan 21 2020
MATHEMATICA
Table[If[n==0, 1, 3*Sum[Binomial[k, n-k]*Binomial[n+k-1, n], {k, 0, n}]], {n, 0, 30}] (* G. C. Greubel, Jan 21 2020 *)
PROG
(Maxima) a(n):=sum((sum(binomial(i, k)*binomial(i+1, n-i), i, k, n))*binomial(n, k), k, 0, n); /* Vladimir Kruchinin, Mar 01 2014 */
(PARI) a(n) = if(n==0, 1, 3*sum(k=0, n, binomial(n+k-1, n)*binomial(k, n-k)) ); \\ Joerg Arndt, Mar 01 2014
(Magma) [1] cat [3*(&+[Binomial(n+k-1, n)*Binomial(k, n-k): k in [0..n]]): n in [1..30]]; // G. C. Greubel, Jan 21 2020
(Sage) [1]+[3*sum(binomial(n+k-1, n)*binomial(k, n-k) for k in (0..n)) for n in (1..30)] # G. C. Greubel, Jan 21 2020
(GAP) Concatenation([1], List([1..30], n-> 3*Sum([0..n], k-> Binomial(n+k-1, n) *Binomial(k, n-k) ))); # G. C. Greubel, Jan 21 2020
CROSSREFS
Sequence in context: A151207 A083881 A151208 * A366118 A362597 A125188
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 28 2000
STATUS
approved