A216703
a(n) = Product_{k=1..n} (49 - 7/k).
Original entry on oeis.org
1, 42, 1911, 89180, 4213755, 200574738, 9594158301, 460519598448, 22162505675310, 1068725273676060, 51619430718553698, 2496503376570051576, 120872371815599997138, 5857661095679076784380, 284096563140435224042430, 13788153197749122873525936
Offset: 0
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seq(product(49-7/k, k=1.. n), n=0..20);
seq((7^n/n!)*product(7*k+6, k=0.. n-1), n=0..20);
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Table[49^n * Pochhammer[6/7, n] / n!, {n, 0, 15}] (* Amiram Eldar, Aug 17 2025 *)
A386274
Expansion of 1/(1 - 49*x)^(5/7).
Original entry on oeis.org
1, 35, 1470, 65170, 2965235, 136993857, 6393046660, 300473193020, 14197358370195, 673585780452585, 32062683149543046, 1530264423046372650, 73197648235718158425, 3507856526988647130675, 168377113295455062272400, 8093326579068206659893360, 389491341617657445507367950
Offset: 0
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CoefficientList[Series[1/(Surd[1-49x,7])^5,{x,0,20}],x] (* Harvey P. Dale, Aug 01 2025 *)
-
my(N=20, x='x+O('x^N)); Vec(1/(1-49*x)^(5/7))
A386271
Expansion of 1/(1 - 49*x)^(2/7).
Original entry on oeis.org
1, 14, 441, 16464, 662676, 27832392, 1201431588, 52862989872, 2359010923038, 106417603861492, 4842000975697886, 221851681068339504, 10223664969232645476, 473434331652157890504, 22014696421825341908436, 1027352499685182622393680, 48092938891512611510804145
Offset: 0
Cf.
A020918 (k=2, m=7),
A020920 (k=2, m=9),
A034835 (k=7, m=1),
A034977 (k=8, m=1),
A035024 (k=9, m=1),
A216702 (k=4, m=3),
A216703 (k=7, m=6),
A354019 (k=6, m=1), this sequence (k=7, m=2),
A386272 (k=7, m=3),
A386273 (k=7, m=4),
A386274 (k=7, m=5).
A386273
Expansion of 1/(1 - 49*x)^(4/7).
Original entry on oeis.org
1, 28, 1078, 45276, 1980825, 88740960, 4037713680, 185734829280, 8613452707860, 401961126366800, 18851976826602920, 887756726925482960, 41946505347229069860, 1987619022607162079520, 94411903573840198777200, 4494006610114793461794720, 214307940219849213209335710
Offset: 0
Showing 1-4 of 4 results.
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