A084641 Binomial transform of n^7.

0, 1, 130, 2574, 25904, 183200, 1040112, 5076400, 22171648, 88915968, 333209600, 1181548544, 4001402880, 13033885696, 41061830656, 125666611200, 374947708928, 1093874155520, 3128047828992, 8785866391552, 24280799641600, 66124498599936, 177683966197760

Offset

0,3

Comments

The binomial transforms of n, n^2, n^3, n^4, n^5, n^6 are A001787, A001788, A058645, A058649, A059338, A056468 respectively.

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-112,448,-1120,1792,-1792,1024,-256).

Formula

a(n) = n^2*(n^5 + 21*n^4 + 105*n^3 + 35*n^2 - 210*n + 112)*2^(n-7).

a(n) = Sum_{k=0..n} C(n, k)*k^7.

G.f.: x*(1+114*x+606*x^2-1168*x^3-96*x^4+816*x^5-272*x^6)/(1-2*x)^8. - Colin Barker, Sep 20 2012

Mathematica

LinearRecurrence[{16, -112, 448, -1120, 1792, -1792, 1024, -256}, {0, 1, 130, 2574, 25904, 183200, 1040112, 5076400}, 41] (* Amiram Eldar, Nov 26 2021 *)

Prog

(Magma) [n^2*(n^5+21*n^4+105*n^3+35*n^2-210*n+112)*2^(n-7): n in [0..40]]; // G. C. Greubel, Mar 20 2023
(SageMath) [n^2*(n^5+21*n^4+105*n^3+35*n^2-210*n+112)*2^(n-7) for n in range(41)] # G. C. Greubel, Mar 20 2023

Crossrefs

Cf. A001015, A001787, A001788, A058645, A058649, A059338, A056468.

Sequence in context: A262108 A250212 A239094 * A271758 A228997 A168124

Adjacent sequences: A084638 A084639 A084640 * A084642 A084643 A084644

Keyword

easy,nonn

Author

Paul Barry, Jun 08 2003

Status

approved