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
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).
Programs
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Magma
[Binomial(n+10, 10)*4^n: n in [0..30]]; // Vincenzo Librandi, Jun 06 2011
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Mathematica
Table[Binomial[n + 10, 10]*4^n, {n, 0, 20}]
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)