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A303488 a(n) = n! * [x^n] 1/(1 - 5*x)^(n/5). 3
1, 1, 14, 312, 9576, 375000, 17873856, 1004306688, 65006637696, 4763494479744, 389812500000000, 35237024762075136, 3487065897634615296, 374960171943074285568, 43532820293400237735936, 5427359437500000000000000, 723181462895975365595529216, 102563963819340862347122245632 (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} (5*k + n).

a(n) = 5^n*Gamma(6*n/5)/Gamma(n/5).

a(n) ~ 6^(6*n/5-1/2)*n^n/exp(n).

EXAMPLE

a(1) = 1;

a(2) = 2*7 = 14;

a(3) = 3*8*13 = 312;

a(4) = 4*9*14*19 = 9576;

a(5) = 5*10*15*20*25 = 375000, etc.

MATHEMATICA

Table[n! SeriesCoefficient[1/(1 - 5 x)^(n/5), {x, 0, n}], {n, 0, 17}]

Table[Product[5 k + n, {k, 0, n - 1}], {n, 0, 17}]

Table[5^n Pochhammer[n/5, n], {n, 0, 17}]

CROSSREFS

Column k=5 of A303489.

Cf. A008546, A008548, A034300, A034301, A034323, A034325, A047055, A047056, A051687, A051688, A051689, A051690, A051691, A052562, A113551, A303486, A303487.

Sequence in context: A034912 A250966 A213466 * A341501 A255857 A239782

Adjacent sequences:  A303485 A303486 A303487 * A303489 A303490 A303491

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 24 2018

STATUS

approved

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Last modified August 19 23:59 EDT 2022. Contains 356231 sequences. (Running on oeis4.)