OFFSET
0,2
LINKS
MathOverflow, Recurrence relation for trinomial Apéry numbers
Eric Weisstein's MathWorld, Apéry Number
FORMULA
a(n) = sum_{k=0..n} ( sum_{l=0..n-k} multinomial(n, [k, l])^2*multinomial(n + k + l, [k, l])^2 ).
a(n) ~ 5 * (1+sqrt(5))^(12*n+6) / (2^(12*n+11) * Pi^3 * n^3). - Vaclav Kotesovec, Feb 19 2015
MAPLE
f:= n -> add(add(combinat:-multinomial(n, k, l, n-k-l)^2*combinat:-multinomial(n+k+l, n, k, l)^2, l=0..n-k), k=0..n):
seq(f(n), n=0..20); # Robert Israel, Feb 19 2015
MATHEMATICA
a[n_] := Sum[Multinomial[k, l, n-k-l]^2*Multinomial[k, l, n]^2, {k, 0, n}, {l, 0, n-k}]; Table[a[n], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jean-François Alcover, Feb 19 2015
STATUS
approved