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A306939 Expansion of 1/((1 - x)^9 - x^9). 3
1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24311, 43776, 75753, 127110, 209475, 346104, 591261, 1081575, 2163150, 4686826, 10656387, 24582663, 56191734, 125640180, 273241161, 577147212, 1184959314, 2369918628, 4631710931, 8881943832, 16798969548, 31537530456 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,2).

FORMULA

a(n) = Sum_{k=0..floor(n/9)} binomial(n+8,9*k+8).

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + 2*a(n-9) for n > 8.

PROG

(PARI) {a(n) = sum(k=0, n\9, binomial(n+8, 9*k+8))}

(PARI) N=66; x='x+O('x^N); Vec(1/((1-x)^9-x^9))

CROSSREFS

Column 9 of A306915.

Cf. A306860.

Sequence in context: A008491 A023034 A000581 * A229889 A243743 A145458

Adjacent sequences:  A306936 A306937 A306938 * A306940 A306941 A306942

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Mar 17 2019

STATUS

approved

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Last modified November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)