A014434 a(n) = Sum_{i=0..n-1} a(i) * a(n-i), a(0) = 1, a(1) = 5.

1, 5, 5, 30, 80, 405, 1505, 7255, 31155, 149455, 688655, 3334880, 15965130, 78294155, 383599455, 1903940030, 9474093880, 47514889255, 239112929655, 1209724381330, 6140755848280, 31294613247255, 159963286607755, 820204107625155, 4216569874416955, 21732350726100905

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1354

Formula

G.f.: (1+x-sqrt(1-2*x-19*x^2))/(2*x). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

G.f.: 1 + 5*x/G(x) with G(x) = (1 - x - 5*x^2/G(x)) (continued fraction). - Nikolaos Pantelidis, Dec 12 2022

D-finite with recurrence: 19*n*a(n) + (3 + 2*n)*a(1 + n) + (-3 - n)*a(n + 2) = 0. - Robert Israel, Apr 29 2026

Maple

f:= gfun:-rectoproc({19*n*a(n) + (3 + 2*n)*a(1 + n) + (-3 - n)*a(n + 2), a(0)=1, a(1)=5}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Apr 29 2026

Crossrefs

Cf. A091148.

Sequence in context: A261569 A117858 A365824 * A375989 A106830 A265798

Adjacent sequences: A014431 A014432 A014433 * A014435 A014436 A014437

Keyword

nonn

Author

Wouter Meeussen

Status

approved