A360775 - OEIS

A360775

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

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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

PROG

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

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

CROSSREFS

Cf. A360774, A360776.

Cf. A360018, A360727.

Sequence in context: A356197 A152410 A177403 * A196523 A260775 A292810

Adjacent sequences: A360772 A360773 A360774 * A360776 A360777 A360778

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 20 2023

STATUS

approved