The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A360775

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A360775

Expansion of Sum_{k>=0} (x * (k + x^2))^k.
(history; published version)

#10 by Michael De Vlieger at Mon Feb 20 07:50:45 EST 2023

STATUS

proposed

approved

#9 by Seiichi Manyama at Mon Feb 20 07:39:20 EST 2023

STATUS

editing

proposed

#8 by Seiichi Manyama at Mon Feb 20 06:18:45 EST 2023

DATA

1, 1, 4, 28, 260, 3152, 46913, 826677, 16823968, 388245283, 10016796672, 285699444297, 8926107792609, 303160590533808, 11120927427841820, 438196895219227683, 18457860168281435172, 827678295600605015006, 39364859979651634985089

#7 by Seiichi Manyama at Mon Feb 20 06:17:35 EST 2023

CROSSREFS

Cf. A360018, A360727.

#6 by Seiichi Manyama at Mon Feb 20 05:55:00 EST 2023

FORMULA

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

#5 by Seiichi Manyama at Mon Feb 20 05:54:23 EST 2023

PROG

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(k+x^2))^k))

#4 by Seiichi Manyama at Mon Feb 20 05:52:47 EST 2023

CROSSREFS

Cf. A360727,.

#3 by Seiichi Manyama at Mon Feb 20 05:52:35 EST 2023

CROSSREFS

Cf. A360774, A360776.

Cf. A360727,

#2 by Seiichi Manyama at Mon Feb 20 05:48:09 EST 2023

NAME

allocated for Seiichi Manyama

Expansion of Sum_{k>=0} (x * (k + x^2))^k.

DATA

1, 1, 4, 28, 260, 3152, 46913, 826677, 16823968, 388245283, 10016796672, 285699444297, 8926107792609, 303160590533808, 11120927427841820

OFFSET

0,3

PROG

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

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Feb 20 2023

STATUS

approved

editing

#1 by Seiichi Manyama at Mon Feb 20 05:48:09 EST 2023

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved