A396238 a(n) = Sum_{i=0..n} Sum_{j=0..i} Sum_{k=0..j} binomial(n+i,2*i) * binomial(i+j,2*j) * binomial(j+k,2*k).

1, 4, 22, 130, 789, 4848, 29975, 185953, 1155696, 7190013, 44757663, 278707048, 1735840329, 10812295670, 67352305826, 419567747884, 2613727621445, 16282589303341, 101435368987532, 631912517383722, 3936637423973502, 24524174461033569, 152779004164967032

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15,-83,220,-303,220,-83,15,-1).

Formula

G.f.: (1-x) * ((1-x)^2 - x) * (((1-x)^2 - x)^2 - x*(1-x)^2) / ((((1-x)^2 - x)^2 - x*(1-x)^2)^2 - x*(1-x)^2*((1-x)^2 - x)^2).

a(n) = 15*a(n-1) - 83*a(n-2) + 220*a(n-3) - 303*a(n-4) + 220*a(n-5) - 83*a(n-6) + 15*a(n-7) - a(n-8).

G.f.: 1 / ( (1-x) * (1-B(x)) * (1-B(B(x))) * (1-B(B(B(x)))) ), where B(x) = x/(1-x)^2.

G.f.: (C(x)/x)^(1/2), where C(x) is the g.f. of A396094.

Prog

(PARI) a(n) = sum(i=0, n, sum(j=0, i, sum(k=0, j, binomial(n+i, 2*i)*binomial(i+j, 2*j)*binomial(j+k, 2*k))));

Crossrefs

Cf. A122367, A166482.

Cf. A396094.

Sequence in context: A370695 A086682 A261399 * A155862 A088536 A066380

Adjacent sequences: A396235 A396236 A396237 * A396239 A396240 A396241

Keyword

nonn

Author

Seiichi Manyama, May 19 2026

Status

approved