A255259 Trinomial generalized Apéry numbers.

1, 9, 721, 82089, 12230001, 2120202009, 406989480241, 84181340789289, 18415254766978801, 4208936841232398009, 996304344364456946721, 242690365333454553543609, 60541628771062122533055441, 15409152448094957808105486009

Offset

0,2

Links

Table of n, a(n) for n=0..13.

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

Cf. A005259.

Sequence in context: A053515 A120816 A161585 * A191367 A189821 A053933

Adjacent sequences: A255256 A255257 A255258 * A255260 A255261 A255262

Keyword

nonn

Author

Jean-François Alcover, Feb 19 2015

Status

approved