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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

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

Cf. A055830, A055834.

Sequence in context: A151207 A083881 A151208 * A125188 A054666 A006026

Adjacent sequences:  A055832 A055833 A055834 * A055836 A055837 A055838

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 28 2000

STATUS

approved

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Last modified May 30 05:35 EDT 2020. Contains 334712 sequences. (Running on oeis4.)