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A213837
Principal diagonal of the convolution array A213836.
4
1, 13, 52, 134, 275, 491, 798, 1212, 1749, 2425, 3256, 4258, 5447, 6839, 8450, 10296, 12393, 14757, 17404, 20350, 23611, 27203, 31142, 35444, 40125, 45201, 50688, 56602, 62959, 69775, 77066, 84848, 93137
OFFSET
1,2
FORMULA
a(n) = n*(5 - 15*n + 16*n^2)/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: f(x)/g(x), where f(x) = x*(1 + 9*x + 6*x^2) and g(x) = (1-x)^4.
a(n) = n*A002412(n) - (n-1)*A002412(n-1). [Bruno Berselli, Dec 11 2012]
a(n) = n*A000384(n) + sum( A000384(i), i=0..n-1 ). [Bruno Berselli, Dec 18 2013]
MATHEMATICA
(See A213836.)
CROSSREFS
Cf. A000384, A002412, A213836, A220084 (for a list of numbers of the form n*P(k,n)-(n-1)*P(k,n-1), where P(k,n) is the n-th k-gonal pyramidal number).
Sequence in context: A183941 A022673 A152742 * A047903 A197790 A317467
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 04 2012
STATUS
approved