A123614 Column 4 of triangle A123610.

1, 5, 39, 175, 618, 1764, 4420, 9900, 20439, 39325, 71603, 124215, 207076, 333200, 520272, 790704, 1173805, 1705725, 2432375, 3409175, 4704846, 6400900, 8596484, 11407500, 14972643, 19452069, 25034835, 31936975, 40410504, 50740800, 63257408, 78330560

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,-4,-4,12,-12,4,12,-22,12,4,-12,12,-4,-4,4,-1).

Formula

G.f.: P_4(x) / ((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2), with P_4(1) = 7!, where P_4(x) = (1+3*x+28*x^2+94*x^3+240*x^4+440*x^5+679*x^6+839*x^7+ 887*x^8+757*x^9+550*x^10+314*x^11+148*x^12+48*x^13+11*x^14+x^15).

Mathematica

CoefficientList[Series[(1 + 3*x + 28*x^2 + 94*x^3 + 240*x^4 + 440*x^5 + 679*x^6 + 839*x^7 + 887*x^8 + 757*x^9 + 550*x^10 + 314*x^11 + 148*x^12 + 48*x^13 + 11*x^14 + x^15)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)^2*(1 - x^4)^2), {x, 0, 50}], x] (* G. C. Greubel, Oct 16 2017 *)
LinearRecurrence[{4, -4, -4, 12, -12, 4, 12, -22, 12, 4, -12, 12, -4, -4, 4, -1}, {1, 5, 39, 175, 618, 1764, 4420, 9900, 20439, 39325, 71603, 124215, 207076, 333200, 520272, 790704}, 40] (* Harvey P. Dale, Feb 04 2023 *)

Prog

(PARI) {a(n)=polcoeff(truncate(Ser([1, 3, 28, 94, 240, 440, 679, 839, 887, 757, 550, 314, 148, 48, 11, 1]))/ ((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2 +x*O(x^n)), n)}

Crossrefs

Cf. A123610 (triangle); columns: A005997, A123613, A123615, A123616.

Sequence in context: A183477 A219086 A064445 * A218918 A075135 A202391

Adjacent sequences: A123611 A123612 A123613 * A123615 A123616 A123617

Keyword

nonn,easy

Author

Paul D. Hanna, Oct 03 2006

Status

approved