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 A303487 a(n) = n! * [x^n] 1/(1 - 4*x)^(n/4). 3
 1, 1, 12, 231, 6144, 208845, 8648640, 422463195, 23781703680, 1515973484025, 107941254220800, 8491022274509775, 731304510986649600, 68444451854354701125, 6916953288171902976000, 750681472158682148959875, 87076954662428278259712000, 10751175443940144673035200625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..17. Index entries for sequences related to factorial numbers FORMULA a(n) = Product_{k=0..n-1} (4*k + n). a(n) = 4^n*Gamma(5*n/4)/Gamma(n/4). a(n) ~ 5^(5*n/4-1/2)*n^n/exp(n). EXAMPLE a(1) = 1; a(2) = 2*6 = 12; a(3) = 3*7*11 = 231; a(4) = 4*8*12*16 = 6144; a(5) = 5*9*13*17*21 = 208845, etc. MATHEMATICA Table[n! SeriesCoefficient[1/(1 - 4 x)^(n/4), {x, 0, n}], {n, 0, 17}] Table[Product[4 k + n, {k, 0, n - 1}], {n, 0, 17}] Table[4^n Pochhammer[n/4, n], {n, 0, 17}] CROSSREFS Column k=4 of A303489. Cf. A000407, A001813, A007696, A008545, A034176, A034177, A047053, A051617, A051618, A051619, A051620, A051621, A051622, A113551, A303486, A303488. Sequence in context: A089370 A171093 A089343 * A280071 A279610 A222702 Adjacent sequences: A303484 A303485 A303486 * A303488 A303489 A303490 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 24 2018 STATUS approved

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Last modified June 25 04:03 EDT 2024. Contains 373697 sequences. (Running on oeis4.)