A036224 Expansion of (-1+1/(1-6*x)^6)/(36*x); related to A036084.

1, 21, 336, 4536, 54432, 598752, 6158592, 60046272, 560431872, 5043886848, 44019376128, 374164697088, 3108445175808, 25311625003008, 202493000024064, 1594632375189504, 12381851383824384, 94927527275986944, 719450733039058944, 5395880497792942080, 40083683697890426880

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (36,-540,4320,-19440,46656,-46656).

Formula

a(n) = 6^(n-1)*binomial(n+6, 5).

G.f.: (-1+(1-6*x)^(-6))/(x*6^2).

From Amiram Eldar, Nov 03 2025: (Start)

Sum_{n>=0} 1/a(n) = 675000*log(6/5) - 123066.

Sum_{n>=0} (-1)^n/a(n) = 399726 - 2593080*log(7/6). (End)

Mathematica

a[n_] := 6^(n-1) * Binomial[n+6, 5]; Array[a, 21, 0] (* Amiram Eldar, Nov 03 2025 *)

Prog

(SageMath) [lucas_number2(n, 6, 0)*binomial(n, 5)/6^7for n in range(6, 24)] # Zerinvary Lajos, Mar 13 2009

Crossrefs

Cf. A036084, A036083.

Sequence in context: A095905 A051525 A107396 * A113895 A062260 A278804

Adjacent sequences: A036221 A036222 A036223 * A036225 A036226 A036227

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved