The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A367473 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A367473

Expansion of e.g.f. 1 / (4 - 3 * exp(x))^3.
(history; published version)

#10 by Michael De Vlieger at Sun Nov 19 08:24:58 EST 2023

STATUS

proposed

approved

#9 by Seiichi Manyama at Sun Nov 19 08:02:42 EST 2023

STATUS

editing

proposed

#8 by Seiichi Manyama at Sun Nov 19 06:37:58 EST 2023

DATA

1, 9, 117, 1953, 39645, 946089, 25926597, 801869553, 27618402285, 1048096422009, 43444114011477, 1952712851250753, 94592798546953725, 4912513525545837129, 272265236648295312357, 16039329591716508497553, 1000809252891040145821965

#7 by Seiichi Manyama at Sun Nov 19 06:37:26 EST 2023

PROG

(PARI) a(n) = sum(k=0, n, 3^k*(k+2)!*stirling(n, k, 2))/2;

#6 by Seiichi Manyama at Sun Nov 19 05:33:04 EST 2023

CROSSREFS

Cf. A226515, A367471.

#5 by Seiichi Manyama at Sun Nov 19 05:32:23 EST 2023

FORMULA

a(0) = 1; a(n) = 3*Sum_{k=1..n} (2 * k/n + 1) * binomial(n,k) * a(n-k).

#4 by Seiichi Manyama at Sun Nov 19 05:30:43 EST 2023

FORMULA

a(n) = (1/2) * Sum_{k=0..n} 3^k * (k+2)! * Stirling2(n,k).

a(0) = 1; a(n) = 3*Sum_{k=1..n} (2 * k/n + 1) * binomial(n,k) * a(n-k).

a(0) = 1; a(n) = 9*a(n-1) - 4*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k).

#3 by Seiichi Manyama at Sun Nov 19 05:27:40 EST 2023

CROSSREFS

Cf. A032033, A367472.

#2 by Seiichi Manyama at Sun Nov 19 05:26:39 EST 2023

NAME

allocated for Seiichi Manyama

Expansion of e.g.f. 1 / (4 - 3 * exp(x))^3.

DATA

OFFSET

0,2

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Nov 19 2023

STATUS

approved

editing

#1 by Seiichi Manyama at Sun Nov 19 05:26:39 EST 2023

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved