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A084901
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a(n) = 4^(n-2)*n*(5*n+3)/2.
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5
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0, 1, 13, 108, 736, 4480, 25344, 136192, 704512, 3538944, 17367040, 83623936, 396361728, 1853882368, 8573157376, 39258685440, 178241142784, 803158884352, 3594887626752, 15994458210304, 70781061038080, 311711546474496
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OFFSET
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0,3
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COMMENTS
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Binomial transform of A084900. Third binomial transform of heptagonal numbers A000566. Fourth binomial transform of (0,1,5,0,0,0,...).
Coefficients in the hypergeometric series identity 1 - 13*x/(x + 12) + 108*x*(x - 1)/((x + 12)*(x + 16)) - 736*x*(x - 1)*(x - 2)/((x + 12)*(x + 16)*(x + 20)) + ... = 0, valid in the half-plane Re(x) > 0. Cf. A276289 and A077616. - Peter Bala, May 30 2019
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LINKS
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FORMULA
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G.f.: x*(1+x)/(1-4*x)^3.
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MATHEMATICA
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Table[2^(2*n-5)*n*(5*n+3), {n, 0, 30}] (* G. C. Greubel, Jun 06 2019 *)
LinearRecurrence[{12, -48, 64}, {0, 1, 13}, 30] (* or *) CoefficientList[ Series[-((x (1+x))/(-1+4 x)^3), {x, 0, 30}], x] (* Harvey P. Dale, Jul 14 2021 *)
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PROG
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(PARI) vector(30, n, n--; 2^(2*n-5)*n*(5*n+3)) \\ G. C. Greubel, Jun 06 2019
(Magma) [2^(2*n-5)*n*(5*n+3): n in [0..30]]; // G. C. Greubel, Jun 06 2019
(Sage) [2^(2*n-5)*n*(5*n+3) for n in (0..30)] # G. C. Greubel, Jun 06 2019
(GAP) List([0..30], n-> 2^(2*n-5)*n*(5*n+3)) # G. C. Greubel, Jun 06 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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