A090408
a(n) = Sum_{k=0..n} binomial(4n+3,4k).
Original entry on oeis.org
1, 36, 496, 8256, 130816, 2098176, 33550336, 536887296, 8589869056, 137439215616, 2199022206976, 35184376283136, 562949936644096, 9007199321849856, 144115187807420416, 2305843010287435776, 36893488143124135936, 590295810375885520896, 9444732965670570950656
Offset: 0
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Table[Sum[Binomial[4n+3,4k],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Feb 12 2020 *)
A345455
a(n) = Sum_{k=0..n} binomial(5*n+1,5*k).
Original entry on oeis.org
1, 7, 474, 12393, 427351, 13333932, 430470899, 13733091643, 439924466026, 14072420067757, 450374698997499, 14411355379952868, 461170414282959151, 14757375158697584607, 472236871202375365274, 15111570273013075344193, 483570355262634763462351
Offset: 0
Sum_{k=0..n} binomial(b*n+c,b*k):
A082311 (b=3,c=1),
A090407 (b=4,c=1),
A070782 (b=5,c=0), this sequence (b=5,c=1),
A345456 (b=5,c=2),
A345457 (b=5,c=3),
A345458 (b=5,c=4).
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a[n_] := Sum[Binomial[5*n + 1, 5*k], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Jun 20 2021 *)
LinearRecurrence[{21,353,-32},{1,7,474},20] (* Harvey P. Dale, Jul 20 2021 *)
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a(n) = sum(k=0, n, binomial(5*n+1, 5*k));
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my(N=20, x='x+O('x^N)); Vec((1-14*x-26*x^2)/((1-32*x)*(1+11*x-x^2)))
A090411
Expansion of g.f. (1-x)/(1-16*x).
Original entry on oeis.org
1, 15, 240, 3840, 61440, 983040, 15728640, 251658240, 4026531840, 64424509440, 1030792151040, 16492674416640, 263882790666240, 4222124650659840, 67553994410557440, 1080863910568919040, 17293822569102704640, 276701161105643274240, 4427218577690292387840
Offset: 0
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Join[{1, a = 15}, Table[a=16*a, {n,0,30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
Join[{1},NestList[16#&,15,20]] (* Harvey P. Dale, Dec 28 2016 *)
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a(n)=if(n,15<<(4*n-4),1) \\ Charles R Greathouse IV, Jun 10 2011
Showing 1-3 of 3 results.