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URL: https://oeis.org/A247608

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A247608
a(n) = Sum_{k=0..3} binomial(6,k)*binomial(n,k).
9
1, 7, 28, 84, 195, 381, 662, 1058, 1589, 2275, 3136, 4192, 5463, 6969, 8730, 10766, 13097, 15743, 18724, 22060, 25771, 29877, 34398, 39354, 44765, 50651, 57032, 63928, 71359, 79345, 87906, 97062, 106833, 117239, 128300, 140036, 152467, 165613, 179494
OFFSET
0,2
LINKS
C. Krattenthaler, Advanced determinant calculus Séminaire Lotharingien de Combinatoire, B42q (1999), 67 pp, (see p. 54).
FORMULA
G.f.: (1+3*x+6*x^2+10*x^3)/(1-x)^4.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4).
a(n) = (6+31*n-15*n^2+20*n^3)/6.
a(n) = 1+6*Binomial(n,1)+15*Binomial(n,2)+20*Binomial(n,3).
MATHEMATICA
Table[(6 + 31 n - 15 n^2 + 20 n^3)/6, {n, 0, 50}] (* or *) CoefficientList[Series[(1 + 3 x + 6 x^2 + 10 x^3)/(1-x)^4, {x, 0, 50}], x]
PROG
(Magma) [(6+31*n-15*n^2+20*n^3)/6: n in [0..40]];
(Magma) [1+6*Binomial(n, 1)+15*Binomial(n, 2)+20*Binomial(n, 3): n in [0..40]];
(Magma) I:=[1, 7, 28, 84]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]];
(PARI) Vec((1+3*x+6*x^2+10*x^3)/(1-x)^4 + O (x^50)) \\ Michel Marcus, Sep 22 2014
(SageMath) m=3; [sum((binomial(2*m, k)*binomial(n, k)) for k in (0..m)) for n in (0..40)] # Bruno Berselli, Sep 22 2014
CROSSREFS
Sequence in context: A378922 A162595 A073363 * A341136 A166322 A008499
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Sep 22 2014
STATUS
approved