A123613 Column 3 of triangle A123610.

1, 4, 20, 68, 175, 392, 786, 1440, 2475, 4036, 6292, 9464, 13805, 19600, 27200, 36996, 49419, 64980, 84238, 107800, 136367, 170696, 211600, 260000, 316881, 383292, 460404, 549460, 651775, 768800, 902066, 1053184, 1223915, 1416108, 1631700, 1872792, 2141581

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,6,-9,12,-9,6,-6,4,-1).

Formula

G.f.: P_3(x) / ((1-x)^2*(1-x^2)^2*(1-x^3)^2), with P_3(1) = 5!, where P_3(x) = (1+2*x+11*x^2+26*x^3+30*x^4+26*x^5+17*x^6+6*x^7+x^8).

Mathematica

CoefficientList[Series[(1 + 2*x + 11*x^2 + 26*x^3 + 30*x^4 + 26*x^5 + 17*x^6 + 6*x^7 + x^8)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)^2), {x, 0, 50}], x] (* G. C. Greubel, Oct 16 2017 *)
LinearRecurrence[{4, -6, 6, -9, 12, -9, 6, -6, 4, -1}, {1, 4, 20, 68, 175, 392, 786, 1440, 2475, 4036}, 40] (* Harvey P. Dale, Apr 22 2019 *)

Prog

(PARI) {a(n)=polcoeff(truncate(Ser([1, 2, 11, 26, 30, 26, 17, 6, 1]))/((1-x)^2*(1-x^2)^2*(1-x^3)^2 +x*O(x^n)), n)}

Crossrefs

Cf. A123610 (triangle); columns: A005997, A123614, A123615, A123616.

Sequence in context: A319779 A287244 A344993 * A006740 A291526 A303011

Adjacent sequences: A123610 A123611 A123612 * A123614 A123615 A123616

Keyword

nonn,easy

Author

Paul D. Hanna, Oct 03 2006

Status

approved