A172978 a(n) = binomial(n+10, 10)*4^n.

1, 44, 1056, 18304, 256256, 3075072, 32800768, 318636032, 2867724288, 24216338432, 193730707456, 1479398129664, 10848919617536, 76776969601024, 526470648692736, 3509804324618240, 22813728110018560, 144934272698941440, 901813252348968960, 5505807224867389440

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..157

Index entries for linear recurrences with constant coefficients, signature (44,-880,10560,-84480,473088,-1892352,5406720,-10813440,14417920,-11534336,4194304).

Formula

From Amiram Eldar, Mar 27 2022: (Start)

G.f.: 1/(1 - 4*x)^11.

Sum_{n>=0} 1/a(n) = 14269429/63 - 787320*log(4/3).

Sum_{n>=0} (-1)^n/a(n) = 78125000*log(5/4) - 1098284605/63. (End)

Mathematica

Table[Binomial[n + 10, 10]*4^n, {n, 0, 20}]

Prog

(Magma) [Binomial(n+10, 10)*4^n: n in [0..30]]; // Vincenzo Librandi, Jun 06 2011

Crossrefs

Cf. A002697, A038845, A038846, A040075, A045543, A054337, A054338, A054339, A054340

Sequence in context: A295650 A004423 A238601 * A345410 A114170 A130645

Adjacent sequences: A172975 A172976 A172977 * A172979 A172980 A172981

Keyword

nonn,easy

Author

Zerinvary Lajos, Feb 06 2010

Status

approved