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A084641 Binomial transform of n^7. 1
0, 1, 130, 2574, 25904, 183200, 1040112, 5076400, 22171648, 88915968, 333209600, 1181548544, 4001402880, 13033885696, 41061830656, 125666611200, 374947708928, 1093874155520, 3128047828992, 8785866391552, 24280799641600, 66124498599936, 177683966197760 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..22.

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

MATHEMATICA

LinearRecurrence[{16, -112, 448, -1120, 1792, -1792, 1024, -256}, {0, 1, 130, 2574, 25904, 183200, 1040112, 5076400}, 21] (* Amiram Eldar, Nov 26 2021 *)

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

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Last modified August 10 03:38 EDT 2022. Contains 356029 sequences. (Running on oeis4.)