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A112532 First differences of [0, A047970]. 5
1, 1, 3, 9, 29, 101, 379, 1525, 6549, 29889, 144419, 736241, 3947725, 22201549, 130624587, 802180701, 5131183301, 34121977865, 235486915507, 1683925343929, 12458499203901, 95237603403381, 751291094637083, 6108883628141189, 51144808472958709, 440444879385258001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

FORMULA

G.f.: (1-x)^2*( Sum_{n >= 0} x^n/(1 - (n+2)*x) ). - Peter Bala, Jul 09 2014

From Mathew Englander, Feb 28 2021: (Start)

a(n) = A089246(n+2,0) - A089246(n+1,0).

a(n) = n + Sum_{i = 0..n} (n-i-1)^2 * (n-i)^i. (End)

MATHEMATICA

a[n_]:= If[n==0, 1, n + Sum[(i-1)^2*i^(n-i), {i, 0, n}]];

Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jan 12 2022 *)

PROG

(PARI) a(n) = n + sum(i = 0, n, (n-i-1)^2 * (n-i)^i); \\ Michel Marcus, Mar 01 2021

(Sage) [n +sum((j-1)^2*j^(n-j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Jan 12 2022

CROSSREFS

Cf. A047970, A112531, A229046.

First differences of column 0 of triangle A089246 (beginning at row 1). With offset 1, first differences of column 0 of triangle A242431. Second differences of column 0 of triangle A101494.

Sequence in context: A278404 A148941 A079319 * A148942 A109432 A148943

Adjacent sequences:  A112529 A112530 A112531 * A112533 A112534 A112535

KEYWORD

nonn

AUTHOR

Alford Arnold, Sep 10 2005

EXTENSIONS

Corrected by D. S. McNeil, Aug 20 2010

STATUS

approved

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Last modified September 26 16:09 EDT 2022. Contains 357000 sequences. (Running on oeis4.)