A306463 a(n) = Sum_{k=0..n} Sum_{m=0..floor(k/2)} binomial(k-m, m)*binomial(n-k, k-m)^2.

1, 1, 2, 6, 15, 37, 98, 262, 699, 1883, 5110, 13918, 38045, 104355, 287028, 791320, 2186209, 6051113, 16776022, 46577806, 129491865, 360432855, 1004332322, 2801307498, 7820572153, 21851390549, 61101872126, 170977916730, 478755116117, 1341389394715, 3760507521800

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..2202

Formula

G.f.: 1/sqrt(x^6 + 2*x^5 - x^4 - 4*x^3 - x^2 - 2*x + 1).

D-finite with recurrence: n*a(n) +(-2*n+1)*a(n-1) +(-n+1)*a(n-2) +2*(-2*n+3)*a(n-3) +(-n+2)*a(n-4) +(2*n-5)*a(n-5) +(n-3)*a(n-6)=0. - R. J. Mathar, Jan 16 2020

Prog

(Maxima)
a(n):=sum(sum(binomial(k-m, m)*binomial(n-k, k-m)^2, m, 0, k/2), k, 0, n);
(PARI) a(n) = sum(k=0, n, sum(m=0, k\2, binomial(k-m, m)*binomial(n-k, k-m)^2)); \\ Michel Marcus, Feb 18 2019
(PARI) N=66; x='x+O('x^N); Vec(1/sqrt(x^6+2*x^5-x^4-4*x^3-x^2-2*x+1)) \\ Seiichi Manyama, Feb 20 2019

Crossrefs

Cf. A008459, A306504.

Sequence in context: A300344 A018019 A331347 * A034518 A260787 A290762

Adjacent sequences: A306460 A306461 A306462 * A306464 A306465 A306466

Keyword

nonn

Author

Vladimir Kruchinin, Feb 17 2019

Status

approved