

A139698


Binomial transform of [1, 25, 25, 25, ...].


7



1, 26, 76, 176, 376, 776, 1576, 3176, 6376, 12776, 25576, 51176, 102376, 204776, 409576, 819176, 1638376, 3276776, 6553576, 13107176, 26214376, 52428776, 104857576, 209715176, 419430376, 838860776, 1677721576, 3355443176, 6710886376, 13421772776, 26843545576
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OFFSET

1,2


COMMENTS

The binomial transform of [1, c, c, c, ...] has the terms a(n)=1c+c*2^(n1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c2)x}/{(2x1)(x1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly.  R. J. Mathar, May 11 2008


LINKS



FORMULA

a(n) = 3*a(n1)2*a(n2). G.f.: x*(23*x+1) / ((x1)*(2*x1)).  Colin Barker, Mar 11 2014


EXAMPLE

a(3) = 76 = (1, 2, 1) dot (1, 25, 25) = (1 + 50 + 25).


MAPLE



MATHEMATICA

LinearRecurrence[{3, 2}, {1, 26}, 40] (* Harvey P. Dale, Jul 25 2021 *)


PROG

(PARI) Vec(x*(23*x+1)/((x1)*(2*x1)) + O(x^100)) \\ Colin Barker, Mar 11 2014


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



