OFFSET
0,3
COMMENTS
Hankel transform is 3^n.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^(n+j)*binomial(k+j, j)*binomial(n, k). - G. C. Greubel, Apr 30 2019
a(n) ~ 3^n / sqrt(3*Pi*n). - Vaclav Kotesovec, Jul 20 2019
MATHEMATICA
a[n_]:= Sum[(-1)^n*Sum[(-1)^j*Binomial[k+j, j], {j, 0, k}]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Apr 30 2019 *)
PROG
(PARI) {a(n) = sum(k=0, n, sum(j=0, k, (-1)^(n+j)*binomial(k+j, j)* binomial(n, k)))}; \\ G. C. Greubel, Apr 30 2019
(Magma) [ (&+[ (&+[(-1)^(n+j)*Binomial(k+j, j)*Binomial(n, k): j in [0..k]]): k in [0..n]]) : n in [0..30]]; // G. C. Greubel, Apr 30 2019
(Sage) [sum(sum((-1)^(n+j)*binomial(k+j, j)*binomial(n, k) for j in (0..k)) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Apr 30 2019
(GAP) List([0..30], n-> Sum([0..n], k-> Sum([0..k], j-> (-1)^(n+j)* Binomial(k+j, j)*Binomial(n, k)))) # G. C. Greubel, Apr 30 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Mar 29 2007
EXTENSIONS
Terms a(10) onward added by G. C. Greubel, Apr 30 2019
STATUS
approved