The On-Line Encyclopedia of Integer Sequences (OEIS)

A360934 revision #8

A360934

Expansion of e.g.f. Sum_{k>=0} exp((4^k-1)*x) * x^k/k!.

1, 1, 7, 73, 1711, 75121, 6743287, 1169659513, 412296162271, 284887781497441, 400134611520973927, 1108533158650520901673, 6238465090832886119430031, 69421876683500992783472318161

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

FORMULA

G.f.: Sum_{k>=0} x^k/(1 - (4^k - 1)*x)^(k+1).

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

PROG

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp((4^k-1)*x)*x^k/k!)))

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(4^k-1)*x)^(k+1)))

(PARI) a(n) = sum(k=0, n, (4^k-1)^(n-k)*binomial(n, k));

CROSSREFS

Cf. A001831, A360933, A360935.

Cf. A135754, A355440.

Sequence in context: A352123 A364938 A134281 * * A215612 A292012

Adjacent sequences: A360931 A360932 A360933 * A360935 A360936 A360937

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Feb 26 2023

STATUS

editing