The On-Line Encyclopedia of Integer Sequences (OEIS)

A367473 revision #10

A367473

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

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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

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).

PROG

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

CROSSREFS

Cf. A032033, A367472.

Cf. A226515, A367471.

Sequence in context: A294190 A113344 A305968 * A375722 A081629 A051617

Adjacent sequences: A367470 A367471 A367472 * A367474 A367475 A367476

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 19 2023

STATUS

approved