A143058 -id:A143058 - cp's OEIS frontend

A143059 A007318 * [1, 10, 25, 15, 1, 0, 0, 0, ...].

1, 11, 46, 121, 252, 456, 751, 1156, 1691, 2377, 3236, 4291, 5566, 7086, 8877, 10966, 13381, 16151, 19306, 22877, 26896, 31396, 36411, 41976, 48127, 54901, 62336, 70471, 79346, 89002, 99481

Offset: 0

Gary W. Adamson, Jul 20 2008

			a(4) = 121 = (1, 3, 3, 1) dot (1, 10, 25, 15) = (1 + 30 + 75 + 15).

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A008278, A143058.

LinearRecurrence[{5,-10,10,-5,1},{1,11,46,121,252},40] (* Harvey P. Dale, May 08 2020 *)

Binomial transform of [1, 10, 25, 15, 1, 0, 0, 0, ...] where (1, 10, 25, 15, 1) = row 5 of triangle A008278.

G.f. ( -1-6*x-x^2+9*x^3-2*x^4 ) / (x-1)^5 . - R. J. Mathar, Apr 04 2012

A143060 A007318 * [1, 15, 65, 90, 31, 1, 0, 0, 0, ...].

Original entry on oeis.org

1, 16, 96, 331, 842, 1782, 3337, 5727, 9207, 14068, 20638, 29283, 40408, 54458, 71919, 93319, 119229, 150264, 187084, 230395, 280950, 339550, 407045, 484335, 572371, 672156, 784746, 911251, 1052836, 1210722

Offset: 1

Gary W. Adamson, Jul 20 2008

			a(3) = 96 = (1, 2, 1) dot (1, 15, 65) = (1 + 30 + 65).

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A143058, A143059, A008278.

Binomial transform of [1, 15, 65, 90, 31, 1, 0, 0, 0, ...] where (1, 15, 65 90, 31, 1) = row 6 of triangle A008278.

G.f.: x*(1+10*x+15*x^2-25*x^3-9*x^4+9*x^5)/(1-x)^6. - Colin Barker, Feb 01 2012

cp's OEIS Frontend

A143059 A007318 * [1, 10, 25, 15, 1, 0, 0, 0, ...].

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