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A096959

Sixth column (m=5) of (1,6)-Pascal triangle A096956.

6, 31, 96, 231, 476, 882, 1512, 2442, 3762, 5577, 8008, 11193, 15288, 20468, 26928, 34884, 44574, 56259, 70224, 86779, 106260, 129030, 155480, 186030, 221130, 261261, 306936, 358701, 417136, 482856, 556512, 638792, 730422, 832167, 944832

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OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = A096956(n+5, 5).

a(n) = 6*b(n) - 5*b(n-1), with b(n) = A000389(n+5) = binomial(n+5, 5).

a(n) = (n+30)*binomial(n+4, 4)/5.

G.f.: (6-5*x)/(1-x)^6.

E.g.f.: x*(720 + 1140*x + 420*x^2 + 45*x^3 + x^4)*exp(x)/120. - G. C. Greubel, Nov 24 2017

From Amiram Eldar, Oct 26 2025: (Start)

Sum_{n>=0} 1/a(n) = 2422342457051813/11063641241212560.

Sum_{n>=0} (-1)^n/a(n) = 1520*log(2)/261 - 6155880174898829/1580520177316080. (End)

MATHEMATICA

Table[(n + 30)*Binomial[n + 4, 4]/5, {n, 0, 50}] (* G. C. Greubel, Nov 24 2017 *)

PROG

(PARI) for(n=0, 30, print1((n+30)*binomial(n+4, 4)/5, ", ")) \\ G. C. Greubel, Nov 24 2017

(Magma) [(n+30)*Binomial(n+4, 4)/5: n in [0..30]]; // G. C. Greubel, Nov 24 2017

CROSSREFS

Cf. A000389, A096956.

Cf. other columns: A096957 (m = 3), A096958 (m = 4), A097297 (m = 6), A097298 (m = 7), A097299 (m = 8), A097300 (m = 9).

Sequence in context: A187508 A087725 A273790 * A112562 A244716 A024447

Adjacent sequences: A096956 A096957 A096958 * A096960 A096961 A096962

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 13 2004

STATUS

approved

URL: https://oeis.org/A096959

⇱ A096959 - OEIS