A143132 - OEIS

A143132

Binomial transform of [1, 5, 15, 35, 70, 0, 0, 0, ...].

1, 6, 26, 96, 321, 876, 2006, 4026, 7321, 12346, 19626, 29756, 43401, 61296, 84246, 113126, 148881, 192526, 245146, 307896, 382001, 468756, 569526, 685746, 818921, 970626, 1142506, 1336276, 1553721, 1796696, 2067126, 2367006, 2698401, 3063446

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OFFSET

1,2

COMMENTS

Conjecture: rightmost digit of terms is cyclic: (1, 6, 6, 6, ... repeat).

LINKS

Table of n, a(n) for n=1..34.

FORMULA

Binomial transform of [1, 5, 15, 35, 70, 0, 0, 0, ...] where (1, 5, 15, 35, 70) = row 4 of triangle A046899.

From R. J. Mathar, Jul 31 2008: (Start)

O.g.f.: (1 + x + 6x^2 + 16x^3 + 46x^4)/(1-x)^5.

a(n) = 46 - 200*n + 330*A000217(n) - 245*A000292(n) + 70*A000332(n+3). (End)

a(n) = (552 - 1190*n + 895*n^2 - 280*n^3 + 35*n^4)/12. - T. D. Noe, Aug 22 2008

EXAMPLE

a(4) = 96 = (1, 3, 3, 1) dot (1, 5, 15, 35) = (1 + 15 + 45 + 35).

CROSSREFS

Cf. A046899.

Sequence in context: A036645 A000393 A106392 * A055589 A318947 A320816

Adjacent sequences: A143129 A143130 A143131 * A143133 A143134 A143135

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jul 27 2008

EXTENSIONS

More terms from T. D. Noe, Aug 22 2008

STATUS

approved