The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A360709 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A360709

Expansion of Sum_{k>=0} (x^3 / (1 - k*x))^k.
(history; published version)

#11 by Vaclav Kotesovec at Fri Feb 17 12:16:00 EST 2023

STATUS

proposed

approved

#10 by Winston de Greef at Fri Feb 17 12:05:18 EST 2023

STATUS

editing

proposed

#9 by Winston de Greef at Fri Feb 17 12:03:49 EST 2023

LINKS

Winston de Greef, <a href="/A360709/b360709.txt">Table of n, a(n) for n = 0..692</a>

STATUS

approved

editing

#8 by Michael De Vlieger at Fri Feb 17 07:38:54 EST 2023

STATUS

proposed

approved

#7 by Seiichi Manyama at Fri Feb 17 04:12:31 EST 2023

STATUS

editing

proposed

#6 by Seiichi Manyama at Fri Feb 17 04:12:23 EST 2023

CROSSREFS

Cf. A078012, A360707.

#5 by Seiichi Manyama at Fri Feb 17 04:04:42 EST 2023

FORMULA

a(n) = Sum_{k=1..floor(n/3)} k^(n-3*k) * binomial(n-2*k-1,k-1) for n > 0.

#4 by Seiichi Manyama at Fri Feb 17 04:01:49 EST 2023

DATA

1, 0, 0, 1, 1, 1, 2, 5, 13, 34, 90, 247, 720, 2256, 7568, 26814, 98982, 377541, 1484254, 6021789, 25271173, 109850447, 494355359, 2298362532, 11008133629, 54175202125, 273460921605, 1414449612648, 7494262602464, 40669492399396, 226002274519733

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x^3/(1-k*x))^k))

(PARI) a(n) = if(n==0, 1, sum(k=1, n\3, k^(n-3*k)*binomial(n-2*k-1, k-1)));

#3 by Seiichi Manyama at Fri Feb 17 03:56:17 EST 2023

CROSSREFS

Cf. A080108, A360708.

#2 by Seiichi Manyama at Fri Feb 17 03:55:04 EST 2023

NAME

allocated for Seiichi Manyama

Expansion of Sum_{k>=0} (x^3 / (1 - k*x))^k.

DATA

OFFSET

0,7

CROSSREFS

Cf. A360707.

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Feb 17 2023

STATUS

approved

editing