A247611 a(n) = Sum_{k=0..6} binomial(12,k)*binomial(n,k).

1, 13, 91, 455, 1820, 6188, 18564, 49596, 119139, 260743, 527065, 996205, 1778966, 3027038, 4942106, 7785882, 11891061, 17673201, 25643527, 36422659, 50755264, 69525632, 93774176, 124714856, 163753527, 212507211, 272824293, 346805641, 436826650

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

C. Krattenthaler, Advanced determinant calculus Séminaire Lotharingien de Combinatoire, B42q (1999), 67 pp, (see p. 54).

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (1 + 6*x + 21*x^2 + 56*x^3 + 126*x^4 + 252*x^5 + 462*x^6) / (1-x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

a(n) = (120 - 8042*n + 20581*n^2 - 17380*n^3 + 7645*n^4 -1518*n^5 + 154*n^6)/120.

Mathematica

Table[(120 - 8042 n + 20581 n^2 - 17380 n^3 + 7645 n^4 - 1518 n^5 + 154 n^6)/120, {n, 0, 40}] (* or *) CoefficientList[Series[(1 + 6 x + 21 x^2 + 56 x^3 + 126 x^4 + 252 x^5 + 462 x^6)/(1 - x)^7, {x, 0, 40}], x]

Prog

(Magma) [(120-8042*n+20581*n^2-17380*n^3+7645*n^4-1518*n^5+ 154*n^6)/120: n in [0..40]];
(Magma) I:=[1, 13, 91, 455, 1820, 6188, 18564]; [n le 7 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..40]];
(Sage) m=6; [sum((binomial(2*m, k)*binomial(n, k)) for k in (0..m)) for n in (0..40)] # Bruno Berselli, Sep 22 2014

Crossrefs

Cf. A005408, A056108, A247608, A247609.

Sequence in context: A212956 A188352 A162631 * A008505 A008495 A010965

Adjacent sequences: A247608 A247609 A247610 * A247612 A247613 A247614

Keyword

nonn,easy

Author

Vincenzo Librandi, Sep 22 2014

Status

approved