A090407
a(n) = Sum_{k = 0..n} C(4*n + 1, 4*k).
Original entry on oeis.org
1, 6, 136, 2016, 32896, 523776, 8390656, 134209536, 2147516416, 34359607296, 549756338176, 8796090925056, 140737496743936, 2251799780130816, 36028797153181696, 576460751766552576, 9223372039002259456
Offset: 0
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Table[Sum[Binomial[4n+1,4k],{k,0,n}],{n,0,30}] (* or *) LinearRecurrence[ {12,64},{1,6},30] (* Harvey P. Dale, Jan 19 2012 *)
A345457
a(n) = Sum_{k=0..n} binomial(5*n+3,5*k).
Original entry on oeis.org
1, 57, 1574, 53143, 1669801, 53774932, 1717012749, 54986385093, 1759098789526, 56296324109907, 1801425114687749, 57646238657975068, 1844672594930734801, 59029601136140621857, 1888946370232447241574, 60446293452901248074943
Offset: 0
Sum_{k=0..n} binomial(b*n+c,b*k):
A090408 (b=4,c=3),
A070782 (b=5,c=0),
A345455 (b=5,c=1),
A345456 (b=5,c=2), this sequence (b=5,c=3),
A345458 (b=5,c=4).
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a[n_] := Sum[Binomial[5*n + 3, 5*k], {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Jun 20 2021 *)
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a(n) = sum(k=0, n, binomial(5*n+3, 5*k));
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my(N=20, x='x+O('x^N)); Vec((1+36*x+24*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.