PROG
(MAGMAMagma) [Binomial(n+4, 5)*(5*(n+2)^4 -35*(n+2)^2 +36)/126: n in [1..30]]; // G. C. Greubel, Aug 28 2019
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(MAGMAMagma) [Binomial(n+4, 5)*(5*(n+2)^4 -35*(n+2)^2 +36)/126: n in [1..30]]; // G. C. Greubel, Aug 28 2019
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1, 36, 381, 2336, 10326, 36552, 110022, 292512, 704847, 1567852, 3263403, 6422208, 12046268, 21675408, 37608828, 63194304, 103199469, 164281524, 255573769, 389409504, 582206130, 855534680, 1237402530, 1763779680, 2480401755, 3444885756, 4729197591, 6422513536, 8634521016, 11499207456
G.f.: (x *(1 + 26*x^2 + 66*x^3 2 + 26*x^4 3 + x^54)/(-1 + - x)^10.
seq(binomial(n+4, 5)*(5*(n+2)^4 -35*(n+2)^2 +36)/126, n=1..30); # G. C. Greubel, Aug 28 2019
Table[n (1 + n) (2 + n) (3 + n) (4 + n) (- 24 + 20 n 20n + 85 n85n^2 + 40 n40n^3 + 5 n5n^4)/15120, {n, 30}] (* or *) Accumulate[Accumulate[Accumulate[Accumulate[Range[24}] ^5]]]] (* or *) CoefficientList[Series[(1 +26x +66x^2 +26x^3 +x^4)/(1-x)^10, {x, 0, 30}], x]
Accumulate[Accumulate[AccumulateNest[Accumulate[, Range[2430]^5]]], 4] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 36, 381, 2336, 10326, 36552, 110022, 292512, 704847, 1567852}, 30] (* _Harvey P. Dale_, May 08 2016 *)
CoefficientList[Series[(1 + 26 x + 66 x^2 + 26 x^3 + x^4)/(- 1 + x)^10, {x, 0, 24}], x]
Nest[Accumulate, Range[30]^5, 4] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 36, 381, 2336, 10326, 36552, 110022, 292512, 704847, 1567852}, 30] (* Harvey P. Dale, May 08 2016 *)
(PARI) vector(30, n, m=n+2; binomial(m+2, 5)*(5*m^4 -35*m^2 +36)/126) \\ G. C. Greubel, Aug 28 2019
(MAGMA) [Binomial(n+4, 5)*(5*(n+2)^4 -35*(n+2)^2 +36)/126: n in [1..30]]; // G. C. Greubel, Aug 28 2019
(Sage) [binomial(n+4, 5)*(5*(n+2)^4 -35*(n+2)^2 +36)/126 for n in (1..30)] # G. C. Greubel, Aug 28 2019
(GAP) List([1..30], n-> Binomial(n+4, 5)*(5*(n+2)^4 -35*(n+2)^2 +36)/126); # G. C. Greubel, Aug 28 2019
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Nest[Accumulate, Range[30]^5, 4] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 36, 381, 2336, 10326, 36552, 110022, 292512, 704847, 1567852}, 30] (* Harvey P. Dale, May 08 2016 *)
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<a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature(10,-45,120,-210,252,-210,120,-45,10,-1).
(10,-45,120,-210,252,-210,120,-45,10,-1).
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<a href="/index/Rec#order_10">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature
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